An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 42
... called a LINEAR COMBINATION of the vectors X1 , ... , X. If a vector x is equal to some linear combination of X1 , ... , X , it is said to be expressible linearly in terms of , or to depend linearly on , X1 , ... , Xk . It is obvious ...
... called a LINEAR COMBINATION of the vectors X1 , ... , X. If a vector x is equal to some linear combination of X1 , ... , X , it is said to be expressible linearly in terms of , or to depend linearly on , X1 , ... , Xk . It is obvious ...
Page 75
... called the ( i , j ) th element of a matrix A will be denoted by A , ; . If , as in ( 3.2.2 ) , A¡¡ aij , we shall write A ( a ) . It is important to remember that the first suffix of an element indicates the row and the second the ...
... called the ( i , j ) th element of a matrix A will be denoted by A , ; . If , as in ( 3.2.2 ) , A¡¡ aij , we shall write A ( a ) . It is important to remember that the first suffix of an element indicates the row and the second the ...
Page 132
... called redundant ( with respect to the system in question . ) It is easy to see that redundant equations can be ... called TRIVIAL ; any other solution is called NON - TRIVIAL . A system of equations not all of which are homogeneous may ...
... called redundant ( with respect to the system in question . ) It is easy to see that redundant equations can be ... called TRIVIAL ; any other solution is called NON - TRIVIAL . A system of equations not all of which are homogeneous may ...
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