Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 64
Gerald Goertzel, Nunzio Tralli. 4.10 The Diagonalization of Normal Matrices - = If A + A = AA + , the matrix A is said to be a normal matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , ...
Gerald Goertzel, Nunzio Tralli. 4.10 The Diagonalization of Normal Matrices - = If A + A = AA + , the matrix A is said to be a normal matrix . Any matrix H which satisfies the condition H H + is called a Hermitian matrix . Clearly , ...
Página 298
... Matrix , 7 adjoint , 56 antisymmetric , 8 characteristic equation of , 27 ... normal , 64 notation , 7-9 null , 11 orthogonal , 56 positive definite , 217 ... Matrix , zero , 11 Method , of images , 123-126 of partial waves , 185-188 pass ...
... Matrix , 7 adjoint , 56 antisymmetric , 8 characteristic equation of , 27 ... normal , 64 notation , 7-9 null , 11 orthogonal , 56 positive definite , 217 ... Matrix , zero , 11 Method , of images , 123-126 of partial waves , 185-188 pass ...
Página 299
... normal , 61 spectral representation of , 60 , 70 Order of diffraction , 196 Orthogonal matrix , 56 Orthogonality , of Bessel functions , 140 of eigenfunctions , 104-105 Orthonormality condition , 54 for spherical harmonics , 153 Parodi ...
... normal , 61 spectral representation of , 60 , 70 Order of diffraction , 196 Orthogonal matrix , 56 Orthogonality , of Bessel functions , 140 of eigenfunctions , 104-105 Orthonormality condition , 54 for spherical harmonics , 153 Parodi ...
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