An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 82
... fact , we can write ABCD for the product in question . Quite generally we may say that in forming products of matrices we need only pay attention to the order of the factors but not to the way in which they are bracketed . We saw above ...
... fact , we can write ABCD for the product in question . Quite generally we may say that in forming products of matrices we need only pay attention to the order of the factors but not to the way in which they are bracketed . We saw above ...
Page 126
... fact in this context is that differentiation and integra- tion are linear operators , i.e. d { αf ( x ) + ẞg ( x ) ... fact . Consider , for example , the class C of all real - valued functions of t and its subclass C ) consisting of those ...
... fact in this context is that differentiation and integra- tion are linear operators , i.e. d { αf ( x ) + ẞg ( x ) ... fact . Consider , for example , the class C of all real - valued functions of t and its subclass C ) consisting of those ...
Page 127
... fact which underlies the theory of the differential equation Ωχ = 0 , since it implies that every linear combination of solutions of the equation is again a solution . The set of all solutions is , in fact , a linear manifold and , as ...
... fact which underlies the theory of the differential equation Ωχ = 0 , since it implies that every linear combination of solutions of the equation is again a solution . The set of all solutions is , in fact , a linear manifold and , as ...
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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Expressions et termes fréquents
A₁ algebra assertion automorphism B₁ basis bilinear form bilinear operator canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix dimensionality E-operations equal equivalence EXERCISE exists follows functions given Hence hermitian form hermitian matrix identity implies inequality integers invariant space isomorphic linear equations linear manifold linear transformation linearly independent matrix group matrix of order minimum polynomial multiplication non-singular linear transformation non-singular matrix non-zero numbers nxn matrix obtain orthogonal matrix positive definite positive semi-definite possesses proof of Theorem prove quadratic form quadric rank relation represented respect result rotation S-¹AS satisfies scalar Show similar singular skew-symmetric matrix solution square matrix suppose symmetric matrix t₁ tion triangular unique unit element unitary matrix V₁ values vector space view of Theorem w₁ write x₁ xTAx y₁ zero