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Math Help - Question about Determinants and invertibility

  1. #1
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    Post Question about Determinants and invertibility

    This is kind of a broad question but I'm looking for kind of a thorough answer. Suppose you computed det(A*transpse(A)) and det(transpose(A)*A) for 10 random 5X6 matrices and 10 random 7X6 matrices. What happens? Can I generalize anything about determinants from this? Does this say anything about Invertibility? I've been finding as I do some calculations with the random matrices that det(A*transpse(A)) and det(transpose(A)*A) seem to equal 0. I'm not sure what this means, am I wrong here? Can this be explained along with the rest of the question?
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  2. #2
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    You understand, do you not, that a matrix A is invertible if and only if det(A) is non-zero? And that det(transpose(A))= det(A) and det(AB)= det(A)det(B) so that det(transpose(A)*A)= det(A*transpose(A))= (det(A))^2= 0 if and only if det(A)= 0? Rather than looking at det(transpose(A)*A) or det(A*transpose(A)), just look at det(A).
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