Linear Algebra with Applications

A₁ A₂ algorithm b₁ b₂ c₁ c₂ coefficient matrix column space column vectors compute condition number coordinate vector corresponding defined denote determine diagonal matrix e₁ e₂ eigenspace is spanned eigenvalues eigenvector eigenvector belonging elementary matrix entries EXAMPLE Exercise factorization form a basis form an orthonormal given Gram-Schmidt process hence Householder transformation inner product space iteration least squares problem linear combination linear operator linear system linear transformation linearly independent m x n matrix MATLAB matrix representing n x n N(AT nonsingular matrix nonzero vector ordered basis orthogonal matrix orthonormal basis orthonormal set P₁ polynomials Proof R(AT real numbers relative error row echelon form row equivalent row operation row space scalar multiplication Section Show singular value decomposition subspace system Ax transition matrix u₁ u₂ upper triangular V₁ V₂ vector space x₁ Y₁ Y₂ zero λ₁