Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 25
... linearly independent eigencolumns . Thus , if A has less than ʼn linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas an arbitrary column is specified by all n ...
... linearly independent eigencolumns . Thus , if A has less than ʼn linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas an arbitrary column is specified by all n ...
Página 28
... linearly dependent and it will be shown that this assumption leads to a contradiction . If the eigencolumns are linearly dependent , there exists a set of numbers a1 , not all zero , such that Σs.iai = 0 ( 2.25 ) The demonstration that ...
... linearly dependent and it will be shown that this assumption leads to a contradiction . If the eigencolumns are linearly dependent , there exists a set of numbers a1 , not all zero , such that Σs.iai = 0 ( 2.25 ) The demonstration that ...
Página 53
... linearly independent vectors in the space , but any n + 1 vectors are linearly dependent . " That this is always possible if the u , are linearly independent may be demonstrated as follows : let u1 , . , u , be linearly independent ...
... linearly independent vectors in the space , but any n + 1 vectors are linearly dependent . " That this is always possible if the u , are linearly independent may be demonstrated as follows : let u1 , . , u , be linearly independent ...
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