Linear Algebra 썸네일형 리스트형 10 Transpose of a matrix Transpose of a matrix Let's define a transpose matrix. Transpose of a transpose matrix A is same with the matrix A! Determinant of transpose Let's assume determinant of any nxn matrix B is equal to the determinant of B's transpose. Then will it be the same if the matrix is (n+1) x (n+1)? Transpose of sums and inverses ) This means that C transpose is equal to the transpose of (A+B)! Rank(a) = ra.. 더보기 09 Linear transformation examples Linear transformation examples: Scaling and reflections Linear transformation examples: Rotations in R2 The rotation of some vector x is going to be equal to a counterclockwise theta degree rotation of x. Rotation in R3 around the x-axis You can generalize in R3. You can try this also in y, z axis. Unit vector unit vector is a vector that has length of 1. At any of dimension, it has length of 1. 더보기 08 Functions and linear transformations A more formal understanding of functions Range: subset of the codomain that the function actually maps to Vector transformation Linear transformations Let's see this Transformation is a lienar treanformation. We have to check the conditions. This conficts with the requirement for a linear tranformation. So this is not a linear transformation! Matrix vector products as linear transformations By m.. 더보기 07 Null space and column space Matrix vector products What we want to do now in this video is relate our notion of a matrix to everything we already know about vectors. Let's define what is means when we take the product of our matrix A with some vector x. Our definition will only work if the vector x has the same number of components as A has columns. This matrix A also can be represented like this. Now the interesting here .. 더보기 이전 1 다음
