SlideShare a Scribd company logo

Vector Spaces

•Download as PPT, PDF•
•
Franklin College Mathematics and Computing Department
Franklin College Mathematics and Computing Department

Carrie Trommater presentation on Vector Spaces for MAT 361 (Modern Algebra), Franklin College, Fall 2009.

EducationTechnologyNews & Politics
1 of 14
Vector Spaces Chapter 18
What is a vector space? ,[object Object]
Proposition 18.1 ,[object Object],For all v in V. For all in F. Then either =0 or v=0 For all v in V. For all in F and all v in V.
Example ,[object Object]
Example ,[object Object]
Subspaces ,[object Object]
Example ,[object Object]
Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object]
Linear Independence ,[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object]
Basis ,[object Object]
Example ,[object Object]
Example ,[object Object]

Recommended

Vector spaces
Vector spaces Vector spaces
Vector spaces
Jitin Pillai
 
Vector space
Vector spaceVector space
Vector space
Mehedi Hasan Raju
 
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchalppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
harshid panchal
 
Independence, basis and dimension
Independence, basis and dimensionIndependence, basis and dimension
Independence, basis and dimension
ATUL KUMAR YADAV
 
Liner algebra-vector space-1 introduction to vector space and subspace
Liner algebra-vector space-1 introduction to vector space and subspace Liner algebra-vector space-1 introduction to vector space and subspace
Liner algebra-vector space-1 introduction to vector space and subspace
Manikanta satyala
 
Vector space
Vector spaceVector space
Vector space
Fukun Master
 
Vector Spaces,subspaces,Span,Basis
Vector Spaces,subspaces,Span,BasisVector Spaces,subspaces,Span,Basis
Vector Spaces,subspaces,Span,Basis
Ravi Gelani
 
Linear algebra-Basis & Dimension
Linear algebra-Basis & DimensionLinear algebra-Basis & Dimension
Linear algebra-Basis & Dimension
Manikanta satyala
 

Recommended

Vector spaces
Vector spaces Vector spaces
Vector spaces
Jitin Pillai
 
Vector space
Vector spaceVector space
Vector space
Mehedi Hasan Raju
 
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchalppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
ppt on Vector spaces (VCLA) by dhrumil patel and harshid panchal
harshid panchal
 
Independence, basis and dimension
Independence, basis and dimensionIndependence, basis and dimension
Independence, basis and dimension
ATUL KUMAR YADAV
 
Liner algebra-vector space-1 introduction to vector space and subspace
Liner algebra-vector space-1 introduction to vector space and subspace Liner algebra-vector space-1 introduction to vector space and subspace
Liner algebra-vector space-1 introduction to vector space and subspace
Manikanta satyala
 
Vector space
Vector spaceVector space
Vector space
Fukun Master
 
Vector Spaces,subspaces,Span,Basis
Vector Spaces,subspaces,Span,BasisVector Spaces,subspaces,Span,Basis
Vector Spaces,subspaces,Span,Basis
Ravi Gelani
 
Linear algebra-Basis & Dimension
Linear algebra-Basis & DimensionLinear algebra-Basis & Dimension
Linear algebra-Basis & Dimension
Manikanta satyala
 
Vector space
Vector spaceVector space
Vector space
Jaimin Patel
 
Vector Space.pptx
Vector Space.pptxVector Space.pptx
Vector Space.pptx
Dr Ashok Tiwari
 
Vector spaces
Vector spacesVector spaces
Vector spaces
Quasar Chunawala
 
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
Sukhvinder Singh
 
Inner Product Space
Inner Product SpaceInner Product Space
Inner Product Space
Patel Raj
 
linear transformation
linear transformationlinear transformation
linear transformation
mansi acharya
 
Eigen values and eigenvectors
Eigen values and eigenvectorsEigen values and eigenvectors
Eigen values and eigenvectors
Amit Singh
 
linear transformation and rank nullity theorem
linear transformation and rank nullity theorem linear transformation and rank nullity theorem
linear transformation and rank nullity theorem
Manthan Chavda
 
Linear transformations and matrices
Linear transformations and matricesLinear transformations and matrices
Linear transformations and matrices
EasyStudy3
 
Inner product spaces
Inner product spacesInner product spaces
Inner product spaces
EasyStudy3
 
P1 . norm vector space
P1 . norm vector spaceP1 . norm vector space
P1 . norm vector space
Anh Phụng Hoàng kim
 
vector space and subspace
vector space and subspacevector space and subspace
vector space and subspace
2461998
 
Echelon and reduced echelon form & Filters
Echelon and reduced echelon form & FiltersEchelon and reduced echelon form & Filters
Echelon and reduced echelon form & Filters
Zahid Ali
 
vector spaces notes.pdf
vector spaces notes.pdfvector spaces notes.pdf
vector spaces notes.pdf
jacky489530
 
Chapter 4: Vector Spaces - Part 1/Slides By Pearson
Chapter 4: Vector Spaces - Part 1/Slides By PearsonChapter 4: Vector Spaces - Part 1/Slides By Pearson
Chapter 4: Vector Spaces - Part 1/Slides By Pearson
Chaimae Baroudi
 
System Of Linear Equations
System Of Linear EquationsSystem Of Linear Equations
System Of Linear Equations
saahil kshatriya
 
Real analysis
Real analysis Real analysis
Real analysis
Kalaiselviprakash
 
Metric space
Metric spaceMetric space
Metric space
NaliniSPatil
 
Matrices and System of Linear Equations ppt
Matrices and System of Linear Equations pptMatrices and System of Linear Equations ppt
Matrices and System of Linear Equations ppt
Drazzer_Dhruv
 
Matrices and determinants
Matrices and determinantsMatrices and determinants
Matrices and determinants
Kum Visal
 
Vector space - subspace By Jatin Dhola
Vector space - subspace By Jatin DholaVector space - subspace By Jatin Dhola
Vector space - subspace By Jatin Dhola
Jatin Dhola
 
Linear vector space
Linear vector spaceLinear vector space
Linear vector space
Safiya Amer
 

More Related Content

What's hot

Eigen values and eigenvectors
Eigen values and eigenvectorsEigen values and eigenvectors
Eigen values and eigenvectors
Amit Singh
 
Linear transformations and matrices
Linear transformations and matricesLinear transformations and matrices
Linear transformations and matrices
EasyStudy3
 
Inner product spaces
Inner product spacesInner product spaces
Inner product spaces
EasyStudy3
 
vector space and subspace
vector space and subspacevector space and subspace
vector space and subspace
2461998
 

What's hot (20)

Vector space
Vector spaceVector space
Vector space
 
Vector Space.pptx
Vector Space.pptxVector Space.pptx
Vector Space.pptx
 
Vector spaces
Vector spacesVector spaces
Vector spaces
 
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
Vcla.ppt COMPOSITION OF LINEAR TRANSFORMATION KERNEL AND RANGE OF LINEAR TR...
 
Inner Product Space
Inner Product SpaceInner Product Space
Inner Product Space
 
linear transformation
linear transformationlinear transformation
linear transformation
 
Eigen values and eigenvectors
Eigen values and eigenvectorsEigen values and eigenvectors
Eigen values and eigenvectors
 
linear transformation and rank nullity theorem
linear transformation and rank nullity theorem linear transformation and rank nullity theorem
linear transformation and rank nullity theorem
 
Linear transformations and matrices
Linear transformations and matricesLinear transformations and matrices
Linear transformations and matrices
 
Inner product spaces
Inner product spacesInner product spaces
Inner product spaces
 
P1 . norm vector space
P1 . norm vector spaceP1 . norm vector space
P1 . norm vector space
 
vector space and subspace
vector space and subspacevector space and subspace
vector space and subspace
 
Echelon and reduced echelon form & Filters
Echelon and reduced echelon form & FiltersEchelon and reduced echelon form & Filters
Echelon and reduced echelon form & Filters
 
vector spaces notes.pdf
vector spaces notes.pdfvector spaces notes.pdf
vector spaces notes.pdf
 
Chapter 4: Vector Spaces - Part 1/Slides By Pearson
Chapter 4: Vector Spaces - Part 1/Slides By PearsonChapter 4: Vector Spaces - Part 1/Slides By Pearson
Chapter 4: Vector Spaces - Part 1/Slides By Pearson
 
System Of Linear Equations
System Of Linear EquationsSystem Of Linear Equations
System Of Linear Equations
 
Real analysis
Real analysis Real analysis
Real analysis
 
Metric space
Metric spaceMetric space
Metric space
 
Matrices and System of Linear Equations ppt
Matrices and System of Linear Equations pptMatrices and System of Linear Equations ppt
Matrices and System of Linear Equations ppt
 
Matrices and determinants
Matrices and determinantsMatrices and determinants
Matrices and determinants
 

Viewers also liked

Maxwell equation
Maxwell equationMaxwell equation
Maxwell equation
Kumar
 
Vector space model of information retrieval
Vector space model of information retrievalVector space model of information retrieval
Vector space model of information retrieval
Nanthini Dominique
 
Document similarity with vector space model
Document similarity with vector space modelDocument similarity with vector space model
Document similarity with vector space model
dalal404
 
Maxwell’s equations
Maxwell’s equationsMaxwell’s equations
Maxwell’s equations
bordoloianup
 

Viewers also liked (20)

Vector space - subspace By Jatin Dhola
Vector space - subspace By Jatin DholaVector space - subspace By Jatin Dhola
Vector space - subspace By Jatin Dhola
 
Linear vector space
Linear vector spaceLinear vector space
Linear vector space
 
Lesson 12: Linear Independence
Lesson 12: Linear IndependenceLesson 12: Linear Independence
Lesson 12: Linear Independence
 
Vector space classification
Vector space classificationVector space classification
Vector space classification
 
Definition ofvectorspace
Definition ofvectorspaceDefinition ofvectorspace
Definition ofvectorspace
 
The vector space model
The vector space modelThe vector space model
The vector space model
 
Maxwell equation
Maxwell equationMaxwell equation
Maxwell equation
 
Vector space model of information retrieval
Vector space model of information retrievalVector space model of information retrieval
Vector space model of information retrieval
 
Document similarity with vector space model
Document similarity with vector space modelDocument similarity with vector space model
Document similarity with vector space model
 
Divergence theorem
Divergence theoremDivergence theorem
Divergence theorem
 
Maxwell’s equations
Maxwell’s equationsMaxwell’s equations
Maxwell’s equations
 
Linear Transformations
Linear TransformationsLinear Transformations
Linear Transformations
 
Lecture7
Lecture7Lecture7
Lecture7
 
Green's theorem in classical mechanics and electrodynamics
Green's theorem in classical mechanics and electrodynamicsGreen's theorem in classical mechanics and electrodynamics
Green's theorem in classical mechanics and electrodynamics
 
Maxwell's equations
Maxwell's equationsMaxwell's equations
Maxwell's equations
 
Integrals and its applications
Integrals and its applicationsIntegrals and its applications
Integrals and its applications
 
ppt on application of integrals
ppt on application of integralsppt on application of integrals
ppt on application of integrals
 
Maths Project Power Point Presentation
Maths Project Power Point PresentationMaths Project Power Point Presentation
Maths Project Power Point Presentation
 
Applications of linear algebra
Applications of linear algebraApplications of linear algebra
Applications of linear algebra
 
Vectors
Vectors Vectors
Vectors
 

Similar to Vector Spaces

Let K be a field. Prove that every not trivial (not necessarily fini.pdf
Let K be a field. Prove that every not trivial (not necessarily fini.pdfLet K be a field. Prove that every not trivial (not necessarily fini.pdf
Let K be a field. Prove that every not trivial (not necessarily fini.pdf
expressionnoveltiesk
 
Ch_12 Review of Matrices and Vectors (PPT).pdf
Ch_12 Review of Matrices and Vectors (PPT).pdfCh_12 Review of Matrices and Vectors (PPT).pdf
Ch_12 Review of Matrices and Vectors (PPT).pdf
Mohammed Faizan
 
MTH285-CH4.5-lecture vector spaces and .ppt
MTH285-CH4.5-lecture vector spaces and .pptMTH285-CH4.5-lecture vector spaces and .ppt
MTH285-CH4.5-lecture vector spaces and .ppt
DrRajendraP
 

Similar to Vector Spaces (10)

Linear algebra
Linear algebraLinear algebra
Linear algebra
 
Linear Algebra for Competitive Exams
Linear Algebra for Competitive ExamsLinear Algebra for Competitive Exams
Linear Algebra for Competitive Exams
 
Linear algebra
Linear algebra Linear algebra
Linear algebra
 
Chapter 4: Vector Spaces - Part 2/Slides By Pearson
Chapter 4: Vector Spaces - Part 2/Slides By PearsonChapter 4: Vector Spaces - Part 2/Slides By Pearson
Chapter 4: Vector Spaces - Part 2/Slides By Pearson
 
Let K be a field. Prove that every not trivial (not necessarily fini.pdf
Let K be a field. Prove that every not trivial (not necessarily fini.pdfLet K be a field. Prove that every not trivial (not necessarily fini.pdf
Let K be a field. Prove that every not trivial (not necessarily fini.pdf
 
Ch_12 Review of Matrices and Vectors (PPT).pdf
Ch_12 Review of Matrices and Vectors (PPT).pdfCh_12 Review of Matrices and Vectors (PPT).pdf
Ch_12 Review of Matrices and Vectors (PPT).pdf
 
150490106037
150490106037150490106037
150490106037
 
MTH285-CH4.5-lecture vector spaces and .ppt
MTH285-CH4.5-lecture vector spaces and .pptMTH285-CH4.5-lecture vector spaces and .ppt
MTH285-CH4.5-lecture vector spaces and .ppt
 
Tot d piffwelsh
Tot d piffwelshTot d piffwelsh
Tot d piffwelsh
 
Vector space interpretation_of_random_variables
Vector space interpretation_of_random_variablesVector space interpretation_of_random_variables
Vector space interpretation_of_random_variables
 

More from Franklin College Mathematics and Computing Department

More from Franklin College Mathematics and Computing Department (6)

Integrating spreadsheets, visualization tools, and computational knowledge en...
Integrating spreadsheets, visualization tools, and computational knowledge en...Integrating spreadsheets, visualization tools, and computational knowledge en...
Integrating spreadsheets, visualization tools, and computational knowledge en...
 
Integrating spreadsheets, visualization tools, and computational knowledge en...
Integrating spreadsheets, visualization tools, and computational knowledge en...Integrating spreadsheets, visualization tools, and computational knowledge en...
Integrating spreadsheets, visualization tools, and computational knowledge en...
 
Matrix Groups and Symmetry
Matrix Groups and SymmetryMatrix Groups and Symmetry
Matrix Groups and Symmetry
 
Taxicab Geometry Presentation
Taxicab Geometry PresentationTaxicab Geometry Presentation
Taxicab Geometry Presentation
 
Group Actions
Group ActionsGroup Actions
Group Actions
 
Integral Domains
Integral DomainsIntegral Domains
Integral Domains
 

Recently uploaded

Gardella_PRCampaignConclusion Pitch Letter
Gardella_PRCampaignConclusion Pitch LetterGardella_PRCampaignConclusion Pitch Letter
Gardella_PRCampaignConclusion Pitch Letter
MateoGardella
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
negromaestrong
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ciinovamais
 

Recently uploaded (20)

Sports & Fitness Value Added Course FY..
Sports & Fitness Value Added Course FY..Sports & Fitness Value Added Course FY..
Sports & Fitness Value Added Course FY..
 
Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104Nutritional Needs Presentation - HLTH 104
Nutritional Needs Presentation - HLTH 104
 
Web & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdfWeb & Social Media Analytics Previous Year Question Paper.pdf
Web & Social Media Analytics Previous Year Question Paper.pdf
 
Gardella_PRCampaignConclusion Pitch Letter
Gardella_PRCampaignConclusion Pitch LetterGardella_PRCampaignConclusion Pitch Letter
Gardella_PRCampaignConclusion Pitch Letter
 
Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1
 
How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17How to Give a Domain for a Field in Odoo 17
How to Give a Domain for a Field in Odoo 17
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
Measures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and ModeMeasures of Central Tendency: Mean, Median and Mode
Measures of Central Tendency: Mean, Median and Mode
 
SECOND SEMESTER TOPIC COVERAGE SY 2023-2024 Trends, Networks, and Critical Th...
SECOND SEMESTER TOPIC COVERAGE SY 2023-2024 Trends, Networks, and Critical Th...SECOND SEMESTER TOPIC COVERAGE SY 2023-2024 Trends, Networks, and Critical Th...
SECOND SEMESTER TOPIC COVERAGE SY 2023-2024 Trends, Networks, and Critical Th...
 
Seal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptxSeal of Good Local Governance (SGLG) 2024Final.pptx
Seal of Good Local Governance (SGLG) 2024Final.pptx
 
Advance Mobile Application Development class 07
Advance Mobile Application Development class 07Advance Mobile Application Development class 07
Advance Mobile Application Development class 07
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptxSOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
SOCIAL AND HISTORICAL CONTEXT - LFTVD.pptx
 
PROCESS RECORDING FORMAT.docx
PROCESS RECORDING FORMAT.docxPROCESS RECORDING FORMAT.docx
PROCESS RECORDING FORMAT.docx
 
Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024Mehran University Newsletter Vol-X, Issue-I, 2024
Mehran University Newsletter Vol-X, Issue-I, 2024
 
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptxBasic Civil Engineering first year Notes- Chapter 4 Building.pptx
Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
 

Vector Spaces