Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 11
... zero is a zero matrix . Zero matrices have the expected properties 0+ m = m 0т = m0 = 0 ( 1.32 ) In ( 1.32 ) the symbol 0 must indicate a zero matrix with the appropriate number of rows and of columns so that the operations are defined ...
... zero is a zero matrix . Zero matrices have the expected properties 0+ m = m 0т = m0 = 0 ( 1.32 ) In ( 1.32 ) the symbol 0 must indicate a zero matrix with the appropriate number of rows and of columns so that the operations are defined ...
Página 28
... zero . As such , the characteristic equation is satisfied by n values of 2 , some of which may be multiple roots ... zero , such that Σsa , = 0 - ( 2.25 ) The demonstration that this leads to an inconsistency is relatively ...
... zero . As such , the characteristic equation is satisfied by n values of 2 , some of which may be multiple roots ... zero , such that Σsa , = 0 - ( 2.25 ) The demonstration that this leads to an inconsistency is relatively ...
Página 249
... zero , whereas all minors of order higher than r are zero , the matrix M is said to be of rank r . Obviously , the rank of a matrix can be zero only if all elements are zero . Suppose now that [ M ] = 0 and that M is of rank r ...
... zero , whereas all minors of order higher than r are zero , the matrix M is said to be of rank r . Obviously , the rank of a matrix can be zero only if all elements are zero . Suppose now that [ M ] = 0 and that M is of rank r ...
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