An Introduction to Linear AlgebraClarendon Press, 1955 - 433 pages |
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Page 153
... variables x1 , ... , x is a polynomial of the type L = L ( x1 , ... , xn ) = a1 x1 + ... + an xn⋅ EXERCISE 5.5.1 . Show that , with respect to obvious definitions of multiplication by scalars and addition , the set of linear forms in n ...
... variables x1 , ... , x is a polynomial of the type L = L ( x1 , ... , xn ) = a1 x1 + ... + an xn⋅ EXERCISE 5.5.1 . Show that , with respect to obvious definitions of multiplication by scalars and addition , the set of linear forms in n ...
Page 360
... variables x , y may be written as ax2 + 2bxy + cy2 . What is the result of applying the substitutions x = ax ' + ẞy ' , y = yx ' + dy ' to the variables ? = We collect below a number of almost obvious results which are implicit in our ...
... variables x , y may be written as ax2 + 2bxy + cy2 . What is the result of applying the substitutions x = ax ' + ẞy ' , y = yx ' + dy ' to the variables ? = We collect below a number of almost obvious results which are implicit in our ...
Page 394
... variables x1 , ... , xn . ( i ) is POSITIVE DEFINITE ( NEGATIVE DEFINITE ) if ☀ > 0 ( p < 0 ) except when x1 = ... = x2 = 0. A form which is positive definite Xn or negative definite is called DEFINITE . Xn ( ii ) is POSITIVE SEMI ...
... variables x1 , ... , xn . ( i ) is POSITIVE DEFINITE ( NEGATIVE DEFINITE ) if ☀ > 0 ( p < 0 ) except when x1 = ... = x2 = 0. A form which is positive definite Xn or negative definite is called DEFINITE . Xn ( ii ) is POSITIVE SEMI ...
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