## Linear Operators: General theory |

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Page 45

2 d . . . . . , in Wig , 19 - - , Qin one ii = 1 in = 1 is called the determinant of the

of the

shall ...

2 d . . . . . , in Wig , 19 - - , Qin one ii = 1 in = 1 is called the determinant of the

**matrix**( au ) . If T is a linear operator , then it can be shown that the determinantsof the

**matrices**of T in terms of any two bases are equal , and so we may andshall ...

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

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Three Basic Principles of Linear Analysis | 49 |

Copyright | |

50 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

analytic applied arbitrary assumed B-space Borel bounded called Chapter clear closed complex condition Consequently constant contains continuous functions continuous linear converges Corollary countably additive defined DEFINITION denote dense determined dimensional disjoint element equation equivalent everywhere Exercise exists extended field finite follows formula function defined function f given Hence Hilbert identity implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear map linear operator linear space meaning metric space neighborhood norm obtained operator positive measure space projection PROOF properties proved range reflexive regular respect satisfies scalar seen separable sequence sequentially set function Show shown statement strongly subset subspace sufficient Suppose Theorem theory tion topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero