## Linear Operators: General theory |

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Page 45

Qi1,19 dinin ii = 1 Σ in = 1 is called the determinant of the

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

terms of any two bases are equal , and so we may and shall call their common ...

Qi1,19 dinin ii = 1 Σ in = 1 is called the determinant of the

**matrix**( a ; ) . If T is alinear operator , then it can be shown that the determinants of the

**matrices**of T interms of any two bases are equal , and so we may and shall call their common ...

Page 564

19 Find the most general solution of the differential equation y ' = Ty where T is

the

systems of n linear homogeneous differential equations , dy ( t ) / dt = A ( t ) y .

Here A ...

19 Find the most general solution of the differential equation y ' = Ty where T is

the

**matrix**of Exercise 5 . The next ten exercises refer to the stability theory ofsystems of n linear homogeneous differential equations , dy ( t ) / dt = A ( t ) y .

Here A ...

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 |

quences | 26 |

Copyright | |

81 other sections not shown

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc proof properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero