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Vector spaces 1 Introduction
Linear dependence dimension of a vector space
45 other sections not shown
algebra basis vectors change of basis characteristic roots coefficients column operations column vector compute converges coordinates Corollary defined definition determinant diagonal entries diagonal matrix dimension echelon matrix elementary row operations example Exercises finite dimensional functions Hence hermitian inner product space integers j-th column Lemma linear combination linear differential equation linear equations linear span linear transformation linear transformation T:V linearly independent m x n method n x n matrix null space number of inversions obtain orthonormal basis permutation plane Principal Axis Theorem principal diagonal prove quadratic form real numbers real symmetric matrix reduced echelon form relative rotation row equivalent row or column row reduced echelon Section semi-definite sequence similar square matrix subspace suppose symmetric matrix Theorem 2.1 tion total number transposition unique unitary matrix upper triangular usual basis vector space zero