Is it always true that det(A^TA)=0, for A=n×m matrix with n<m?

Aryanna Fisher

Aryanna Fisher

Answered question


Is it always true that
det ( A T A ) = 0 , for A = n × m matrix with n < m?

Answer & Explanation



Beginner2022-11-13Added 18 answers

From the way you wrote it, the product is size m .. However, the maximum rank is n . which is smaller. The matrix A T A being square and of non-maximal rank, it has determinant 0..
Rhett Guerrero

Rhett Guerrero

Beginner2022-11-14Added 6 answers

R a n k ( A B ) min ( R a n k A , R a n k B ) Notice that A T A is m × m

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