An Introduction to Linear AlgebraClarendon Press, 1955 - 433 pages |
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Page 132
... solutions of the system ( 5.1.4 ) are precisely the solutions of the single equation x + y = 5. ' DEFINITION 5.1.2 . A SOLUTION of a system of equations in the unknowns x1 , ... , x , is a set of numbers §1 , ... , §n such that every ...
... solutions of the system ( 5.1.4 ) are precisely the solutions of the single equation x + y = 5. ' DEFINITION 5.1.2 . A SOLUTION of a system of equations in the unknowns x1 , ... , x , is a set of numbers §1 , ... , §n such that every ...
Page 133
... solution x1 = $ 1 , ... , Xn = Ax = 0 . En ( of either system ) will , accordingly , be regarded as a column vector ... solution Xo . Then ( i ) any solution of this system is expressible as the sum of x and a suitable solution of Ax 0 ...
... solution x1 = $ 1 , ... , Xn = Ax = 0 . En ( of either system ) will , accordingly , be regarded as a column vector ... solution Xo . Then ( i ) any solution of this system is expressible as the sum of x and a suitable solution of Ax 0 ...
Page 134
... solution of ( 5.1.6 ) . The proof of this result depends on the linearity of the differential operator ƒ ( D ) in ... solution depends on reducing any given system to an equivalent system of this special type , we begin by discussing ...
... solution of ( 5.1.6 ) . The proof of this result depends on the linearity of the differential operator ƒ ( D ) in ... solution depends on reducing any given system to an equivalent system of this special type , we begin by discussing ...
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