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 0m - 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 ...
... zero is a zero matrix . Zero matrices have the expected properties 0+ m = m 0m - 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 ...
Página 246
... zero if any two rows ( or columns ) have corresponding elements propor- tional . V. If all the elements of any row ( or column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero ...
... zero if any two rows ( or columns ) have corresponding elements propor- tional . V. If all the elements of any row ( or column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero ...
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 . | M | 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 . | M | Suppose now that [ M ] = 0 and that M is of rank r ...
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