Well, then this guy is going to be a square matrix.

And if he's a square matrix, what else do we know about it?

Well, if you have x represented in B coordinate system, then you can multiply it times the change of basis matrix, and you can just get regular x. But if have regular x, and you need to find this, one, if C is invertible, then you can apply this equation right here, which isn't always the case. This is only if C is invertible.

If we can assume that these, this is a square matrix with an orthonormal set.

And we also know, since it's a square matrix with linearly independent columns, that C is invertible.

If we have a square matrix with linearly independent columns, it means that C is invertible.

In the last couple of videos, we've seen that if we have some matrix C that is n by n. It's a square matrix, and is columns, column form and orthonormal set.

3v squared minus 2v squared is just v squared.

Area squared is equal to ad minus bc squared.

This is where we need it to be a square matrix where all of its columns are mutually orthogonal and they're all normal.

And this right here, this is C inverse, which is equal to C transpose, because C is an invertible matrix, or a square matrix, with orthonormal columns.

And then you're going to have a plus c squared, d squared.

I don't see any s squared terms there.

That's just alpha over s squared plus alpha squared.

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square kilometers

square centimeters

square millimeters

square feet

sq feet

square inch

square inches

square in

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square miles

So we have our area squared is equal to x minus y squared or ad minus cb, or let me write it, bc squared.

We could rewrite this as y squared over x squared.

This is equal to x squared minus 2 times xy plus y squared.

It's a square image.

The desks are not square.

1 s squared.

3 squared is 9.

So an identity matrix is a matrix.

Let's just do some matrix matrix products.

And that is equal to s a times a over f squared plus a squared.

2nd derivative r squared.

A 2 by 3 matrix, a 2 by 3 times 3 by 2 matrix, I got a 2 by 2 matrix.

The identity matrix times any other matrix is just that matrix.

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That is equal to a dot a, a times a, a squared plus c squared.

So in general, the nullity of any matrix of any matrix

So it's a 2 by 3 matrix.

Anything times that identity matrix is going to be equal to itself.