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Solution for Diagonalizable Matrices
The Evaluation of a Function of a Matrix for an Arbitrary Matrix
Vector Spaces and Linear Operators
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approximate arbitrary base vectors basis Bessel function boundary conditions chap chapter coefficients column commute consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain dual space eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements equations of motion evaluate example expansion finite number follows formal solution formula Fourier given Green's function Hence Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane multiplication nonsingular nonsingular matrix normal Note number of degrees obtained orthonormality conditions perturbation plane procedure relations representation result Ritz method satisfies the boundary scattering sinh solve spherical spherical harmonics Substitution theorem trial functions vanish variable vector space Verify wave whence write written yields York zero