Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 27
... equation Au = λυ ( 2.23 ) for some nonzero u and some number 2. But ( cf. Sec . 1.7 ) the necessary and sufficient ... equation is called the characteristic equation for the matrix A. Sometimes it is known as the secular equation for the ...
... equation Au = λυ ( 2.23 ) for some nonzero u and some number 2. But ( cf. Sec . 1.7 ) the necessary and sufficient ... equation is called the characteristic equation for the matrix A. Sometimes it is known as the secular equation for the ...
Página 28
... equation is satisfied by n values of 2 , some of which may be multiple roots . To summarize , the eigenvalues of an n × n square matrix A are found as the roots of the characteristic equation of A as given in ( 2.24 ) . If the n roots ...
... equation is satisfied by n values of 2 , some of which may be multiple roots . To summarize , the eigenvalues of an n × n square matrix A are found as the roots of the characteristic equation of A as given in ( 2.24 ) . If the n roots ...
Página 238
... equation are the approximate eigen- values 1 = 9 , 22 = 27 which correspond , respectively , to the exact values # 2 and 472 . For n = 4 , h = 1/4 , the determinantal equation 1 / 162-2 1 0 1 1162-2 1 = = 0 0 1 1161-2 * 2 , has ...
... equation are the approximate eigen- values 1 = 9 , 22 = 27 which correspond , respectively , to the exact values # 2 and 472 . For n = 4 , h = 1/4 , the determinantal equation 1 / 162-2 1 0 1 1162-2 1 = = 0 0 1 1161-2 * 2 , has ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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