The Weyr form was discovered by the Jordan canonical form.
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By contrast, the existence of Jordan canonical form for a matrix is a deep theorem.
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To see why equality may not always hold, consider the Jordan canonical form of a matrix in the finite-dimensional case.
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For example, the spectral theory of compact operators on Banach spaces takes a form that is very similar to the Jordan canonical form of matrices.
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*PM : proof of Jordan canonical form theorem, id = 5709-- WP guess : proof of Jordan canonical form theorem-- Status:
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*PM : proof of Jordan canonical form theorem, id = 5709-- WP guess : proof of Jordan canonical form theorem-- Status:
7.
When comparing the two results, a rough analogy can be made with the relationship between the spectral theorem for normal matrices and the Jordan canonical form.
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Note the algorithm does not require that the matrix "'A "'be diagonalizable and bypasses complexities of the Jordan canonical forms normally utilized.
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However, when a matrix " N " is normal, its Jordan canonical form is diagonal ( up to unitary equivalence ); this is the spectral theorem.
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Specifically, applying the structure theorem for finitely generated modules over a principal ideal domain to this algebra yields as corollaries the various canonical forms of matrices, such as Jordan canonical form.
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