## Matrices: An Introductory Course |

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bilinear block matrix characteristic matrix characteristic root closed with respect cofactors column subscripts complex numbers compute congruent containing Corollary corresponding defined denote determinantal polynomial diag diagonal block diagonal element diagonal matrix elementary matrices elementary multiplicative elements in F equations establishes Theorem exercise exists a nonsingular expansion field F Given the matrix greatest common divisor hence identity matrix interchange invariant factors inversion pairs lemma linear forms linear set linear transformation linearly independent m x n matrix matrix with elements monic multiplying n x n determinant n-rowed square matrix nonsingular matrix nonzero normal order number field number of inversions obtained orthogonal matrices pairs of elements partitioned positive definite principal submatrix product of elementary r-rowed rational canonical form real numbers row subscripts set over F singular skew matrix solution subset symmetric matrix Theorem 12 triangular matrix unique write