An Introduction to Linear AlgebraClarendon Press, 1955 - 433 pages |
À l'intérieur du livre
Résultats 1-3 sur 66
Page 148
... once led to the general solution in the form ( 5.3.7 ) . 2 = In § 6.3.2 we shall see how the method for solving systems of linear equations illustrated above can be used with even less labour . 5.4 . Systems of homogeneous linear ...
... once led to the general solution in the form ( 5.3.7 ) . 2 = In § 6.3.2 we shall see how the method for solving systems of linear equations illustrated above can be used with even less labour . 5.4 . Systems of homogeneous linear ...
Page 203
... once again . Among all non - zero polynomials annihilating A we now consider those of least degree , and by multiplying them by suitable non - zero constants we ensure that they are monic ( i.e. they have their leading coefficients ...
... once again . Among all non - zero polynomials annihilating A we now consider those of least degree , and by multiplying them by suitable non - zero constants we ensure that they are monic ( i.e. they have their leading coefficients ...
Page 307
... once that it continues to hold for the latter . 1 The argument is by induction with respect to n and is of the type with which we are now familiar from the proofs of Theorems 10.3.4 , 10.3.7 , and 10.3.8 . Let us assume that the ...
... once that it continues to hold for the latter . 1 The argument is by induction with respect to n and is of the type with which we are now familiar from the proofs of Theorems 10.3.4 , 10.3.7 , and 10.3.8 . Let us assume that the ...
Table des matières
PART | 3 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
11 autres sections non affichées
Autres éditions - Tout afficher
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