- #1
sihag
- 29
- 0
Suppose A : n x n
A is invertible iff the columns (and rows) of A are linearly independent
A is invertible
iff det |A| is non-zero
iff rank A is n
iff column rank is n
iff dim (column space is n)
iff the n columns of A are linearly independent
Well, this is a proof that I laid down. It was junked by my prof. She said I have to use linear transformations to prove it. Someone throw some light ?
A is invertible iff the columns (and rows) of A are linearly independent
A is invertible
iff det |A| is non-zero
iff rank A is n
iff column rank is n
iff dim (column space is n)
iff the n columns of A are linearly independent
Well, this is a proof that I laid down. It was junked by my prof. She said I have to use linear transformations to prove it. Someone throw some light ?