Sylvester's Law of Inertia

Herausgegeben:Surhone, Lambert M.; Timpledon, Miriam T.; Marseken, Susan F.

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Betascript Publishing
• Seitenzahl: 116
• Englisch
• Abmessung: 220mm
• ISBN-13: 9786131234927
• ISBN-10: 6131234922
• Artikelnr.: 30116933