## An introduction to the algebra of matrices with some applications |

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### Contents

DEFINITIONS AND PRELIMINARY NOTIONS | 1 |

DETERMINANTS AND THE INVERSE OF A MATRIX | 27 |

THE THEORY OF LINEAR EQUATIONS | 44 |

Copyright | |

9 other sections not shown

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### Common terms and phrases

adjugate matrix arbitrary axis characteristic equation characteristic roots characteristic vectors coefficients cofactors conic Consider coordinate axes coordinate vectors critical minor dependent determinant diagonal form diagonal matrix dimensionality displacement elementary matrices example EXERCISE expressed factors fixed axes given Hence homogeneous equations inner product interchange inverse ith row jth column linear combination linear equations linear transformation linearly independent lower triangular matrix algebra matrix of order method non-singular non-zero normal equations null matrix number of unknowns observation equations obtained orthogonal matrix orthonormal partitioned permutation plane positive definite premultiply quadratic form rank reader rectangular reduced respectively result rigid body rotation of axes row and jth rows and columns rows columns satisfied scalar skew-symmetric matrix solution square matrix sub-matrices Suppose symmetric matrix total number transpose triangular matrix unique unit matrix unit vector upper triangular values vector space write zero