Let A be an m×n matrix, then ( ).
A:
AAT =ATA.
B:
if rank(A) = m, then AT A is invertible.
C:
if rank(A) = n, then AAT is invertible.
D:
if rank(A) = n, then AT A is invertible.
A:
AAT =ATA.
B:
if rank(A) = m, then AT A is invertible.
C:
if rank(A) = n, then AAT is invertible.
D:
if rank(A) = n, then AT A is invertible.
举一反三
- Let A be a n×n matrix, then ( ) A: AAT =ATA. B: det(AAT ) = det(AT A). C: if det(A) = 0, then A is invertible. D: if det(A) = 0, then AT is invertible.
- If I-AB is invertible, then I-BA is invertible. Where I is the identity matrix, and A is m by n, B is n by m.
- Let A be a n×n matrix, then ( ) A: [img=94x23]180348ef1e7493d.png[/img] B: [img=171x28]180348ef2664920.png[/img] C: If [img=85x25]180348ef2f7cdbe.png[/img], then [img=14x19]180348ef37b5dfe.png[/img] is invertible. D: If [img=85x25]180348ef2f7cdbe.png[/img], then [img=22x23]180348ef47fab11.png[/img]is invertible.
- If A and B are m × n matrices then have the same rank, then the rank of AB must equal the rank of BA.
- Let A be a 4 by 3 matrix, and r(A)=2, and B is an invertible matrix, then r(AB)=______