Linear Operators: General theory |
From inside the book
Results 1-3 of 31
Page 45
... matrix ( a ;; ) . 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 ...
... matrix ( a ;; ) . 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 ...
Page 564
... matrix differential equation dY / dt = A ( t ) Y where a solution is a n × n complex valued matrix Y ( t ) , differentiable and satisfying the differential equation for each te I. Show that for each to e I and each complex ( constant ) ...
... matrix differential equation dY / dt = A ( t ) Y where a solution is a n × n complex valued matrix Y ( t ) , differentiable and satisfying the differential equation for each te I. Show that for each to e I and each complex ( constant ) ...
Page 607
... 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 . Sylvester [ 1 , 2 ] constructed arbitrary ...
... 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 . Sylvester [ 1 , 2 ] constructed arbitrary ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ