## Linear Operators, Part 1 |

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Page 45

If T is a linear operator, then it can be shown that the determinants of the

of T in terms of any two bases are equal, and so we may and shall call their

common value the determinant of T, denoted by det (T). The determinant satisfies

the ...

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 call their

common value the determinant of T, denoted by det (T). The determinant satisfies

the ...

Page 564

w 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)\,. Here A(t)

...

w 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)\,. Here A(t)

...

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

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero