Sylvester Matrix
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Sylvester matrix is a matrix associated to two polynomials that provides information about those polynomials. It is named for James Joseph Sylvester. These matrices are used in commutative algebra, e.g. to test if two polynomials have a (non constant) common factor. In such a case, the determinant of the associated Sylvester matrix (which is named the resultant of the two polynomials) equals zero. The converse is also true. The solutions of the simul...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a Sylvester matrix is a matrix associated to two polynomials that provides information about those polynomials. It is named for James Joseph Sylvester. These matrices are used in commutative algebra, e.g. to test if two polynomials have a (non constant) common factor. In such a case, the determinant of the associated Sylvester matrix (which is named the resultant of the two polynomials) equals zero. The converse is also true. The solutions of the simultaneous linear equations Consequently the rank of the Sylvester matrix determines the degree of the greatest common divisor of p and q.
