FINITE MATRICES SIMILAR TO IRREDUCIBLE ONES
نویسندگان
چکیده
منابع مشابه
Matrices Similar to Partial Isometries
We determine when a matrix is similar to a partial isometry, refining a result of Halmos–McLaughlin.
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Let IF be field, and let A and B be n X n matrices with elements in IF. Suppose that A is completely reducible and that B is symmetric. If the principal minors of A determined by the 1and 2-circuits of the graph of B and by the chordless circuits of the graph of A are equal to the corresponding principal minors of B, then A is diagonally similar to B; and conversely.
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As we will see, modular arithmetic aids in testing the irreducibility of polynomials and even in completely factoring polynomials in Z[x]. If we expect a polynomial f(x) is irreducible, for example, it is not unreasonable to try to find a prime p such that f(x) is irreducible modulo p. If we can find such a prime p and p does not divide the leading coefficient of f(x), then f(x) is irreducible ...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2000
ISSN: 1027-5487
DOI: 10.11650/twjm/1500407262