HGK_Studio

________________________________________________________________________________________________ MIT Gilbert Strang : Lecture 14 ( Orthogonal Vectors and Subspaces ) https://www.youtube.com/watch?v=YzZUIYRCE38&list=PL49CF3715CB9EF31D&index=14 Orthogonal vectors & Subspaces nullspace ⊥ row space N(A^T * A) = N(A)  * The angle between the two sub-spaces is 90 degrees (Orthogonal) Orthogonal vectors Pythagoras figured out that vectors x and y are orthogonal when x^T * y = 0 * So, 2 x^T * y = 0, when they are orthogonal ** Subspace S is orthogonal to subspace T means : every vector in S is orthogonal to every vector in T * for the case of orthogonal, they don't intersect in any non-zero vector. row space is orthogonal to nullspace. why? Ax = 0, so dot products of (row of A) · x = 0 which means the null space of x is orthogonal to every row. null space and row space are orthogonal complements in R^n Null space contains all vectors ⊥ row space. Comming : Ax = b   wh...