why if a matrices is not invertible then its not absolute positive

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- October 2nd 2011, 05:38 AMtransgalacticinvertible to positive absolute link
why if a matrices is not invertible then its not absolute positive

? - October 2nd 2011, 08:24 AMDevenoRe: invertible to positive absolute link
positive-definite matrices cannot be singular. suppose so, then for a positive-definite matrix A, there is some x ≠ 0, with Ax = 0. hence x^T(Ax) = 0, contradicting the fact that A is positive-definite.

since a positive-definite matrix is non-singular, it posseses an inverse, so any non-invertible matrix cannot possibly be positive-definite. - October 2nd 2011, 09:37 AMtransgalacticRe: invertible to positive absolute link
yes i understand now

if its definite positive then all of its eigenvalues are positive

T(v)=kv the only way for T(v)=0 is that v=0

so the kerT={0}

so its invertible

but our A is not invertible so its not definite positive

correct?

thanks:) - October 2nd 2011, 10:16 AMDevenoRe: invertible to positive absolute link
that is a valid argument also.