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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх