Let A be the following symmetric matrix

A =

[4 2 -2 2

2 2 1 1

-2 1 14 -1

2 1 -1 x]

find the values of x , such that A is positive definite.

Printable View

- Oct 26th 2008, 08:59 AMtinngpositive definite matrix
Let A be the following symmetric matrix

A =

[4 2 -2 2

2 2 1 1

-2 1 14 -1

2 1 -1 x]

find the values of x , such that A is positive definite. - Oct 26th 2008, 10:16 AMmathemanyakanswer
a

**symmetric matrix**is a square matrix,*A*, that is equal to its transpose http://upload.wikimedia.org/math/a/f...b50df7fdfd.png and An*n*×*n*real symmetric matrix*M*is*positive definite*if*z*T*Mz*> 0 for all non-zero vectors*z*with real entries (i.e.*z*∈**R***n*), where*z*T denotes the transpose of*z*. - Oct 26th 2008, 10:57 AMLaurent
There is a theorem telling that (here, ) is positive definite if, and only if, for the determinant of is positive.

If you know this, then it is easy. The determinants of are positive, they do not depend on , and the determinant of is found to be , hence it is positive iff . So is positive definite iff .