Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 16
... inverse it is nonsingular , and ( 2 ) if m is nonsingular , it has a unique inverse . Thus , suppose that there exist a pair of matrices p and m such that pm I. Then , m is nonsingular ; as the following shows = so that | pm | \ m ...
... inverse it is nonsingular , and ( 2 ) if m is nonsingular , it has a unique inverse . Thus , suppose that there exist a pair of matrices p and m such that pm I. Then , m is nonsingular ; as the following shows = so that | pm | \ m ...
Página 101
... inverse transformation is given by a matrix T : or f ( x ) = ft ( x , y ) F ( y ) dy f = TF Substitution of ( 8.18 ) into ( 8.19 ) yields ог f ( x ) = [ [ [ 1 ( x , y ) 5 ( y , x ' ) dy ] f ( x ' ) dx ' f = TSƒ It then follows that one ...
... inverse transformation is given by a matrix T : or f ( x ) = ft ( x , y ) F ( y ) dy f = TF Substitution of ( 8.18 ) into ( 8.19 ) yields ог f ( x ) = [ [ [ 1 ( x , y ) 5 ( y , x ' ) dy ] f ( x ' ) dx ' f = TSƒ It then follows that one ...
Página 228
... inverse the eigenvalue problem ( 16.1 ) may be replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration ... Inverses by Iteration The problem of finding the inverse 228 APPROXIMATE METHODS.
... inverse the eigenvalue problem ( 16.1 ) may be replaced by the problem L ̄1y = λ ̃1y ( 16.8 ) Clearly , the largest eigenvalue of -1 to which the iteration ... Inverses by Iteration The problem of finding the inverse 228 APPROXIMATE METHODS.
Contenido
34 | 12 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх