Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 7
... diagonal elements of m . A matrix all of whose off- diagonal elements are zeros is called a diagonal matrix . Any matrix m for which m1 = m ,,, ij FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 7.
... diagonal elements of m . A matrix all of whose off- diagonal elements are zeros is called a diagonal matrix . Any matrix m for which m1 = m ,,, ij FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 7.
Página 26
... diagonal matrix ( with diagonal elements 2. ) is introduced as1 [ ƒ ( A ) ] ;; = ƒ ( 2 ; ) 8 ;; ( 2.18 ) Then the definition of s becomes As sɅ = ( 2.19 ) where A is specified to be diagonal . Further f ( A ) s = sf ( A ) ( 2.20 ) ...
... diagonal matrix ( with diagonal elements 2. ) is introduced as1 [ ƒ ( A ) ] ;; = ƒ ( 2 ; ) 8 ;; ( 2.18 ) Then the definition of s becomes As sɅ = ( 2.19 ) where A is specified to be diagonal . Further f ( A ) s = sf ( A ) ( 2.20 ) ...
Página 30
... diagonal matrix . In step 3a , in place of sr 1 , one finds the matrix d1r such that sd d − 1r = 1 . The answer , as given in step 4a , becomes sde ^ t d - 1r . But e is a diagonal matrix and all diagonal matrices commute with each ...
... diagonal matrix . In step 3a , in place of sr 1 , one finds the matrix d1r such that sd d − 1r = 1 . The answer , as given in step 4a , becomes sde ^ t d - 1r . But e is a diagonal matrix and all diagonal matrices commute with each ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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