## The Theory of MatricesThis volume offers a concise overview of matrix algebra's many applications, discussing topics of extensive research and supplying proofs. Its contents include reviews of matrices, arrays, and determinants; the characteristic equation; associated integral matrices; equivalence, congruence, and similarity; composition of matrices; matric equations; functions of matrices; and matrices of infinite order. 1946 edition. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Matrices Arrays and Determinants | 1 |

Total niatric algebra | 2 |

Diagonal and scalar matrices | 5 |

Determinants | 6 |

Properties of determinants | 8 |

Rank and nullity | 10 |

Identities among minors | 12 |

Reducibility | 14 |

Linear form moduls | 37 |

Ideals | 38 |

Equivalence | 40 |

Invariant factors and elementary divisors | 43 |

Factorization of a matrix | 44 |

29 Polynomial domains | 45 |

Equivalent pairs of matrices | 48 |

Automorphic transformations | 50 |

Arrays and determinants of higher dimension | 15 |

Matrices in noncommutative systems | 16 |

The characteristic equation | 17 |

15 Determination of the minimum equation | 20 |

Characteristic roots | 22 |

Conjugate sets | 24 |

Limits for the characteristic roots | 25 |

Characteristic roots of unitary matrices | 28 |

HI Associated Integral Matrices | 29 |

Construction of unimodular matrices | 31 |

Greatest common divisors | 35 |

Congruence | 51 |

33 Matrices with rational integral elements | 54 |

Matrices with elements in a field | 56 |

35 Matrices in an algebraically closed field | 60 |

Hermitian matrices | 62 |

Automorphs | 65 |

Similarity | 68 |

Composition of matrices | 81 |

Matric equations | 89 |

Functions of Matrices | 97 |

Matrices of infinite order | 104 |

### Common terms and phrases

Acta math Akad Amer array Atti Accad automorph Autonne Bull C. R. Acad called canonical form Cayley characteristic equation characteristic roots coefficients commutative companion matrix complex field congruent converges Corollary corresponding defined definition degree Dickson direct sum edition elementary divisors elementary transformations equivalent finite number Frobenius Hence hermitian matrix infinite order invariant factors Kronecker Lincei linear linearly independent Loewy London Math main diagonal matric algebra matrices with elements matrix of order minimum equation minor determinants Moderne Algebra modul multiplication necessary and sufficient non-singular matrix normal form obtained orthogonal matrix pairs of matrices Palermo Vol Paris Vol Philos polynomial preuB principal ideal ring Proc proof proved rank q rational integral elements reine angew Rend rows and columns scalar singular skew matrix solution sufficient condition Sylvester symmetric matrix Theorem Toeplitz Trans Unabridged republication unimodular matrix unique unitary matrix Univ Waerden Wiss