Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 26
... diagonalizable . This definition implies that the eigencolumns of a diagonalizable matrix form a complete set and vice versa . It has been previously remarked that not all matrices are diagonalizable . Specifically , as the reader will ...
... diagonalizable . This definition implies that the eigencolumns of a diagonalizable matrix form a complete set and vice versa . It has been previously remarked that not all matrices are diagonalizable . Specifically , as the reader will ...
Página 27
... diagonalizable . ( The bar denotes complex conjugate . ) Another class of matrices for which diagonalizability is assured is determined by the following : If all the eigenvalues of A are distinct , so that A has n different eigenvalues ...
... diagonalizable . ( The bar denotes complex conjugate . ) Another class of matrices for which diagonalizability is assured is determined by the following : If all the eigenvalues of A are distinct , so that A has n different eigenvalues ...
Página 35
... diagonalizable Α = SAT ST = 1 then this solution may be written u ( t ) = { Suct1T , M ( 0 ) + Σ Sat2s [ ' ell - F ( 3 ) ds k.j SikT = Σ Sue's ' Σ Trs [ u , √ ( 0 ) + [ ' e ̄1oF , ( 5 ) ds ] Exercises 1. Diagonalize the matrix M = 669 ...
... diagonalizable Α = SAT ST = 1 then this solution may be written u ( t ) = { Suct1T , M ( 0 ) + Σ Sat2s [ ' ell - F ( 3 ) ds k.j SikT = Σ Sue's ' Σ Trs [ u , √ ( 0 ) + [ ' e ̄1oF , ( 5 ) ds ] Exercises 1. Diagonalize the matrix M = 669 ...
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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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