Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 18
... independent if there exists no linear combination of these columns which vanishes ; that is , the k n - columns m , are linearly independent if there exists no set of k numbers x , not all zero such that Im Σmixi 0 i = 1 ( 1.48 ) The ...
... independent if there exists no linear combination of these columns which vanishes ; that is , the k n - columns m , are linearly independent if there exists no set of k numbers x , not all zero such that Im Σmixi 0 i = 1 ( 1.48 ) The ...
Página 25
... 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 an arbitrary column is specified by all n elements ...
... 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 an arbitrary column is specified by all n elements ...
Página 53
... 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 lincarly independent , and let x be ...
... 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 lincarly independent , and let x be ...
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