Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 23
... eigencolumns such that u ( 0 ) may be written as a linear combination ( superposition ) of these eigencolumns . In such a case , a solution almost as simple in form as that of ( 2.9 ) is obtained . Thus , let the eigencolumns of A be ...
... eigencolumns such that u ( 0 ) may be written as a linear combination ( superposition ) of these eigencolumns . In such a case , a solution almost as simple in form as that of ( 2.9 ) is obtained . Thus , let the eigencolumns of A be ...
Página 25
... eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than n linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas ...
... eigencolumns of A if and only if A has n linearly independent eigencolumns . Thus , if A has less than n linearly independ- ent eigencolumns , the resultant linear superposition will depend on less than n arbitrary constants , whereas ...
Página 28
... eigencolumns are 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 Σsa , = 0 - ( 2.25 ) The ...
... eigencolumns are 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 Σsa , = 0 - ( 2.25 ) The ...
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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Términos y frases comunes
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