Sylvester's Criterion
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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, Sylvester''s criterion is a necessary and sufficient criterion to determine whether a Hermitian matrix is positive-definite. It is named after James Joseph Sylvester.Sylvester''s criterion states that a Hermitian matrix M is positive-definite if and only if all the following matrices have a positive determinant:The proof is only for nonsingular Hermitian matrix with coefficients in Rnxn, therefore only for nonsingular real-symmetric matricesStatement III: If the real-symmetric matrix A is positive definite then A possess factorization of the form A=BTB, where B is nonsingular (Theorem I), the expression A=BTB implies thah A possess factorization of the form A=RTR (Statement II), therefore all the leading principal minors of A are positive (Statement I).
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GarantieWeitere Informationen
- Allgemeine Informationen
- GTIN 09786131234507
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131234507
- Format Fachbuch
- Titel Sylvester's Criterion
- Herausgeber Betascript Publishing
- Anzahl Seiten 128
- Genre Mathematik
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