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Applied Mathematical Methods by Bhaskar Dasgupta

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13

Eigenvalue Problem of General Matrices

In this chapter, we complete our discussion of the algebraic eigenvalue problem through a cursory overview of methods applied for non-symmetric (general) matrices. On the one hand, here we discuss ‘methods for general matrices’, while on the other we study the method of inverse iteration, which is ‘a general method applicable to all kinds of matrices’.

Introductory Remarks

As discussed in Chap. 9, a general matrix need not be diagonalizable. Therefore, we try to triangularize it, so as to at least capture the eigenvalues. In the presence of complex eigenvalues, it may not even have a triangular form, if we insist on using real arithmetic only. Even if a given matrix is triangularizable in R, or even diagonalizable, ...

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