Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 14
... nonsingular matrices is nonsingular ( this is a stronger state- ment than that the product is nonzero ) . Further , the same nonsingular matrix may be canceled from both sides of an equation ( provided it appears on the extreme left or ...
... nonsingular matrices is nonsingular ( this is a stronger state- ment than that the product is nonzero ) . Further , the same nonsingular matrix may be canceled from both sides of an equation ( provided it appears on the extreme left or ...
Página 16
... nonsingular matrices is non- singular . Let then pq = r | p | [ q ] = | r | whence if then Ipl # 0 [ r ] 0 The following portions of this section will show ( 1 ) that if m has an inverse it is nonsingular , and ( 2 ) if m is nonsingular ...
... nonsingular matrices is non- singular . Let then pq = r | p | [ q ] = | r | whence if then Ipl # 0 [ r ] 0 The following portions of this section will show ( 1 ) that if m has an inverse it is nonsingular , and ( 2 ) if m is nonsingular ...
Página 18
... nonsingular matrix has rank n , since the nonvanishing of the determinant of m implies that the only solution of mx = O is x 0 ( see property 3 ) . Furthermore , if m is an n n matrix of rank n , it is nonsingular , as follows again ...
... nonsingular matrix has rank n , since the nonvanishing of the determinant of m implies that the only solution of mx = O is x 0 ( see property 3 ) . Furthermore , if m is an n n matrix of rank n , it is nonsingular , as follows again ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх