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Sylvester's Law of Inertia
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Sylvester''s law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant under a change of coordinates. Namely, if A is the symmetric matrix that defines the quadratic form, and S is any invertible matrix such that D = SAST is diagonal, then the number of negative elements in the diagonal of D is always the same, for all such S; and the same goes for the number of positive elements.This property is named for J. J. Sylvester who published its proof in 1852.Let A be a symmetric square matrix of order n with real entries. Any non-singular matrix S of the same size is said to transform A into another symmetric matrix B = SAST, also of order n, where ST is the transpose of S. If A is the coefficient matrix of some quadratic form of Rn, then B is the matrix for the same form after the change of coordinates defined by S.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131234927
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Größe H220mm x B220mm
- EAN 9786131234927
- Format Fachbuch
- Titel Sylvester's Law of Inertia
- Herausgeber Betascript Publishing
- Anzahl Seiten 116
- Genre Mathematik
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