An Introduction to Linear AlgebraClarendon Press, 1955 - 433 pages |
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Page 73
... unique solution for x , which 1 is denoted by x = or 1 / a or a - 1 . The number a - 1 is called the a inverse or reciprocal of a . For a 0 the equation ax = b has the b unique solution x = a - 1b which is usually denoted by - or b / a ...
... unique solution for x , which 1 is denoted by x = or 1 / a or a - 1 . The number a - 1 is called the a inverse or reciprocal of a . For a 0 the equation ax = b has the b unique solution x = a - 1b which is usually denoted by - or b / a ...
Page 91
... unique solution ( 3.6.3 ) . If | A | 0 , then , by virtue of Theorem 3.5.2 , the matrix X given by ( 3.6.3 ) satisfies AX = XA = I , and is therefore a solution of both ( 3.6.1 ) and ( 3.6.2 ) . To show that this solution is unique ...
... unique solution ( 3.6.3 ) . If | A | 0 , then , by virtue of Theorem 3.5.2 , the matrix X given by ( 3.6.3 ) satisfies AX = XA = I , and is therefore a solution of both ( 3.6.1 ) and ( 3.6.2 ) . To show that this solution is unique ...
Page 92
... unique inverse number a - 1 having the property that aa - 1 1. As we have seen , every non- = a - la = singular square matrix A possesses a unique inverse such that AA - 1 A - 1A = I. EXERCISE 3.6.1 . Show that I - 1 assuming that α1 ...
... unique inverse number a - 1 having the property that aa - 1 1. As we have seen , every non- = a - la = singular square matrix A possesses a unique inverse such that AA - 1 A - 1A = I. EXERCISE 3.6.1 . Show that I - 1 assuming that α1 ...
Table des matières
PART | 3 |
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 C₁ 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 isomorphic linear combination 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 nxn matrix obtain orthogonal matrix positive definite possesses proof of Theorem prove quadratic form quadric rank reduces 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 values vector space view of Theorem w₁ write x₁ y₁ zero α₁