Plant propagation: Sexual and Asexual propapagation.pptx
Linear Algebra
1. 6.837 Linear Algebra Review Patrick Nichols Thursday, September 18, 2003 6.837 Linear Algebra Review
2.
3.
4.
5.
6.
7.
8.
9.
10. Vectors: Dot Product 6.837 Linear Algebra Review Think of the dot product as a matrix multiplication The magnitude is the dot product of a vector with itself The dot product is also related to the angle between the two vectors – but it doesn’t tell us the angle
11.
12.
13.
14. Determinant of a Matrix 6.837 Linear Algebra Review Sum from left to right Subtract from right to left Note: N! terms
15.
16.
17.
18. Orthonormal Basis 6.837 Linear Algebra Review X, Y, Z is an orthonormal basis. We can describe any 3D point as a linear combination of these vectors. How do we express any point as a combination of a new basis U, V, N , given X, Y, Z ?
19. Orthonormal Basis 6.837 Linear Algebra Review (not an actual formula – just a way of thinking about it) To change a point from one coordinate system to another, compute the dot product of each coordinate row with each of the basis vectors.
![Overview ,[object Object],[object Object],[object Object],[object Object],[object Object],6.837 Linear Algebra Review](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)