Monday, July 16, 2007

A singular matrix

They call me A and I am square
Of order 3 by 3
But I have a little secret
That it won't take long to see

I cannot be inverted
Whatever method you try
I have no power to the minus one
And here is the reason why

For I am not of full rank
Correlation between my columns is one
Some call me singular
And my determinant is none

I've got linear dependence across and down
That's all there is to be said
I just cannot be reciprocated
Or stood upon my head

Transpose me if you will
The result will be just the same
It won't make any difference
If my rows and columns are exchanged

I am a singular matrix and that is that
You can add to me or subtract
I can be multiplied too when I am conformable
But not inverted, and that's a fact.