## Determinants and Matrices |

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### Contents

CONTENTS CHAPTER I | 1 |

The Notation of Matrices | 3 |

Matrices Row and Column Vectors Scalars | 4 |

42 other sections not shown

### Common terms and phrases

according to elements adjugate compound algebra bialternant bilinear form Binet-Cauchy theorem bordered determinant called Cauchy expansion coefficients cofactors column suffixes column vector complementary minor conjugate permutations denoted derived determinant of order diagonal elements diagonal matrix elementary operations equal equations Ax evaluate example expressed extensional factor Hence Hermitian form Hermitian matrix identity interchange ith row Jacobi's theorem kth compound Laplacian expansion latent roots linear transformation linearly dependent matrix notation matrix of order minor of order natural order nonsingular nonzero number of inversions number of terms order nxn order r+1 orthogonal partitioned matrices polynomial premultiplying principal diagonal principal minors product matrix prove quadratic form rank reader reciprocal matrix respect result row suffixes row vector rows and columns rows or columns scalar simultaneous equations skew Hermitian solution square matrix submatrix Sylvester's theorem symmetric matrix transposed transposition unitary unitary matrix vanish variables Wronskian x'Ax zero