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MATRICES AMD SYSTEMS OF EQUATIONS
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algorithm arithmetic augmented matrix back substitution Chapter coefficient matrix column space column vectors compute condition number coordinate vector corresponding denote det(A determine diagonal elements diagonal matrix dimension eigenspace is spanned eigenvalues eigenvector eigenvector belonging elementary matrix entries EXAMPLE Exercise Figure floating-point numbers form a basis form an orthonormal function Gram-Schmidt process hence Householder transformation inner product space inverse iteration least squares problem linear combination linear operator linear system linear transformation linearly independent MATLAB matrix and let matrix of rank matrix representing method N(AT nonsingular matrix nonzero vector ordered basis orthogonal matrix orthonormal basis orthonormal set pivot element pivotal row Proof Prove quadratic R(AT real numbers reduced row echelon relative error respect row echelon form row equivalent row operation row space scalar multiplication Section Show singular value decomposition spanning set system Ax th row transition matrix upper triangular vector space verify zero