Linear Operators: General theory |
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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 565
... 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 n × n constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ...
... 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 n × n constant , non- singular matrix . 26 Let A ( t ) have period p > 0 ...
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 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ