## Linear Operators: General theory |

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Page 45

In air , 1 , ... , di non in - 1 is called the determinant of the

In air , 1 , ... , di non in - 1 is called the determinant of the

**matrix**( ai ) . If T is a linear operator , then it can be shown that the determinants of the**matrices**of T in terms of any two bases are equal , and so we may and shall ...Page 565

Show that the set of all non - singular

Show that the set of all non - singular

**matrix**solutions are precisely the**matrices**Y ( t ) C where C is any nxn ... If y ( t ) is a non - singular solution**matrix**of DY | dt = A ( t ) Y then show that Y ( t + p ) = Y ( t ) C for some ...Page 607

Polynomials of a

Polynomials of a

**matrix**were used almost from the beginning of the theory , and by 1867 Laguerre [ 1 ] had considered infinite power series in a**matrix**in constructing the exponential function of a**matrix**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero