Invertible Matrix

If A is an Invertible Matrix, Show that det(A^T A)>0

4 Answers

262

Aditya Bhutra ·2012-04-13 13:00:47

det(A^T) = det (A) (transposing)

det(A^TA) = det(A^T)*det(A) = {det(A)}² >0

since det(A)â‰ 0 as the matrix is invertible

@aditya, what if the matrix have imaginary terms?

then (det A)² can be negative ...?

johncenaiit
That is the question? if the elements from complex numbers
this will not excepted.

but complex number matrices are also invertible, if detâ‰ 0

so you must specify its a real matrix...

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