## Linear Operators: General theory |

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Page 45

With this notation the number expressed by the sum i = 1 din , . . . , in Qi1 , 19 . . . ,

dinin is = 1 mai is called the determinant of the

operator , then it can be shown that the determinants of the

of ...

With this notation the number expressed by the sum i = 1 din , . . . , in Qi1 , 19 . . . ,

dinin is = 1 mai is called the determinant of the

**matrix**( aij ) . If T is a linearoperator , then it can be shown that the determinants of the

**matrices**of T in termsof ...

Page 565

25 Let Y ( t ) be a solution

Show that the set of all non - singular

Y ( t ) C where C is any nxn constant , nonsingular

period p ...

25 Let Y ( t ) be a solution

**matrix**of dY / dt = A ( t ) Y which is non - singular .Show that the set of all non - singular

**matrix**solutions are precisely the**matrices**Y ( t ) C where C is any nxn constant , nonsingular

**matrix**. 26 Let A ( t ) haveperiod p ...

Page 607

Polynomials of a

by 1867 Laguerre [ 1 ] had considered infinite power series in a

constructing the exponential function of a

arbitrary ...

Polynomials of a

**matrix**were used almost from the beginning of the theory , andby 1867 Laguerre [ 1 ] had considered infinite power series in a

**matrix**inconstructing the exponential function of a

**matrix**. Sylvester [ 1 , 2 ] constructedarbitrary ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero