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 k 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 k Σmixi = 0 i = 1 ( 1.48 ) The ...
Página 25
... 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 elements ...
... 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 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 linearly independent , and let x ...
... 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 , and let x ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх