Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 14
... exists such that = I where I is the unit matrix . Thus , suppose that m exists . Then qm = pqm = - p ( qm ) = pl ( pq ) m = = Om = P 0 so that p = 0 , which is clearly false . Thus , no such m exists . A useful manner in which to define ...
... exists such that = I where I is the unit matrix . Thus , suppose that m exists . Then qm = pqm = - p ( qm ) = pl ( pq ) m = = Om = P 0 so that p = 0 , which is clearly false . Thus , no such m exists . A useful manner in which to define ...
Página 16
... exists a q I , second that there exists a p such that pm = such that mq that p = 9 . = To find q such that mg = I , and third I , one need merely solve the equations for each of the n columns of q in turn . These are mq.i = di for the ...
... exists a q I , second that there exists a p such that pm = such that mq that p = 9 . = To find q such that mg = I , and third I , one need merely solve the equations for each of the n columns of q in turn . These are mq.i = di for the ...
Página 18
... exists no linear combination of these columns which vanishes ; that is , the k n - columns m , are linearly independent if there exists no set of k numbers x , not all zero such that Im Σmixi 0 i = 1 ( 1.48 ) The rank of a matrix may ...
... exists no linear combination of these columns which vanishes ; that is , the k n - columns m , are linearly independent if there exists no set of k numbers x , not all zero such that Im Σmixi 0 i = 1 ( 1.48 ) The rank of a matrix may ...
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