# Linear Independence of Vectors over C

1. Jan 30, 2010

### sir_manning

Hi

I just want to confirm something. I have $$A,B\in M_{nm}(\mathbb{C})$$ and I want to prove they are linearly independent. Since they are over the complex field, do I have to prove:

$$(a_1+ib_1)A+(a_2+ib_2)B=0 \ \Leftrightarrow \ a_1=a_2=b_1=b_2=0$$ ?

Thanks.

2. Jan 30, 2010

### VeeEight

Yes this is what you want to show