Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 12
... ( column ) x . The result is a 1 × 1 matrix zx given by ZX n Σzixi i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then multiply ...
... ( column ) x . The result is a 1 × 1 matrix zx given by ZX n Σzixi i = 1 ( 1.37 ) In words the prescription becomes : To multiply the row z into the column x , multiply the leftmost element of z by the topmost element of x ; then multiply ...
Página 25
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
... column u as a linear combination of the eigenvectors of A suffices to enable the evaluation of f ( A ) and the solution of the initial value problems earlier considered . It will now be shown that an arbitrary column u may be written as ...
Página 246
... column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero , because each term contains one factor from the row ( or column ) of zeros . VI . If each element of any row ( or column ) ...
... column ) are zero , the value of the determinant is zero . Each term of the expansion of the determinant is zero , because each term contains one factor from the row ( or column ) of zeros . VI . If each element of any row ( or column ) ...
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