## Latent roots and latent vectors |

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### Contents

APPLICATIONS OP LATENT ROOTS AND | 20 |

Axes of symmetry of a conic section Jacobi and GaussSeidel methods | 26 |

THE METHOD OF DANILEVSKY | 39 |

Copyright | |

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An-r calculations required Chapter characteristic equation clearly correct to four corresponding latent vector Danilevsky's method deflation example 6.1 Exercises find the latent following matrices four decimal places Frobenius form Frobenius matrix Gauss-Seidel method gives Hessenberg form Householder's method hyperbola induction the theorem inverse iteration iterative method Jacobi Krylov's method largest modulus latent roots leading diagonal linearly independent latent matrix given method of Givens method of Householder method of Lanczos minimal polynomial Muller's method multiplications non-zero number of calculations orthogonal matrix previous vectors Proof Q-R algorithm reduce reference required tridiagonal roots and vectors roots of largest rotating rounding errors sequence Show similarity transformation solution Solve the equations starting vector Sturm series Sturm's theorem symmetric matrix take the matrix theorem 1.5 theorem is proved tridiagonal form tridiagonal matrix unitary matrix upper triangular matrix Yr+1 zero