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 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
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