June 2006
Intermediate to advanced
515 pages
16h 22m
English
Content preview from Applied Mathematical MethodsBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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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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