Dot product: x1y1 + x2y2 + ... xkyk
Length of a vector x in Rn
Distance between two points x, y:
A unit vector is a vector x with length ||x|| = sqrt(x*x) = 1
Two vectors x and y are orthogonal or perpendicular if x dot y = 0
6.2 Orthogonal Complements
Orthogonal complement: subpace of V is the orthogonal complement of subpace of Z if every vectors in V is orthogonal to every vectors in Z
Let A be a matrix and let W = Col ( A ) . Then
W perp = Nul(A transpose)
A transpose means turning everything into parametric form
Row space of a matrix A is the span of the rows of A and is Row(A)
6.3 Orthogonal Projections
Let W be a subspace of R n and let x be a vector in R n . We denote the closest vector to x on W by x W .
x_wperp = x-x_w
Compute projection with a known X:
Compute projection with an unknown X:
6.4 Orthogonal Sets
6.5 The Method of Least Squares
