Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 18
... linear superposition of the columns of the matrix . To proceed further , it is useful to introduce the concept of linear inde- pendence . A set of n columns is said to be linearly independent if there exists no linear combination of ...
... linear superposition of the columns of the matrix . To proceed further , it is useful to introduce the concept of linear inde- pendence . A set of n columns is said to be linearly independent if there exists no linear combination of ...
Página 25
... linear combination of the 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 ...
... linear combination of the 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 ...
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 lincarly independent , and ...
... 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 lincarly independent , and ...
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