Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 11
... further in Sec . 1.5 . The definition will be given here . The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then ...
... further in Sec . 1.5 . The definition will be given here . The product of two matrices is defined only if the number of columns in the matrix on the left is equal to the number of rows in the matrix on the right . The product is then ...
Página 14
... further that no matrix m exists such that qm = I where I is the unit matrix . Thus , suppose that m exists . Then pqm = = p ( qm ) = pl = р = ( pq ) m = Om = 0 so that p = 0 , which is clearly false . Thus , no such m exists . A useful ...
... further that no matrix m exists such that qm = I where I is the unit matrix . Thus , suppose that m exists . Then pqm = = p ( qm ) = pl = р = ( pq ) m = Om = 0 so that p = 0 , which is clearly false . Thus , no such m exists . A useful ...
Página 55
... further restricted . If u ; that and u ; + form a bi - orthonormal basis , then the dual basis ut is such Further , if u , * u , = 8¡¡ Sij v ; = Σ uxtxi the dual vectors v ; + are given by ( 4.7 ) : v ; † = Σ ¿ ¿ ‚ ut 1 Or a change from ...
... further restricted . If u ; that and u ; + form a bi - orthonormal basis , then the dual basis ut is such Further , if u , * u , = 8¡¡ Sij v ; = Σ uxtxi the dual vectors v ; + are given by ( 4.7 ) : v ; † = Σ ¿ ¿ ‚ ut 1 Or a change from ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх