Ax=B question

[markraz]

Hi are these essentially the same thing??

(A^T A)^-1 * A^T(b) = x

or

(A^T A) ∗ x = A^T(b)


thanks

 

[Steven G]

Sure looks that way to me.

 

[Dr.Peterson]

Hi are these essentially the same thing??

(A^T A)^-1 * A^T(b) = x

or

(A^T A) ∗ x = A^T(b)

I'd say they are equivalent if A^T A is invertible. But that's almost obvious.

But you haven't told us what any of these entities are. I assume A is a matrix; is it square? Is it invertible? (If so, more interesting things can be done.) I assume b and x are column matrices. And so on ...

Is there a context to your question? Do you have a goal?

 

[markraz]

I'd say they are equivalent if A^T A is invertible. But that's almost obvious.

But you haven't told us what any of these entities are. I assume A is a matrix; is it square? Is it invertible? (If so, more interesting things can be done.) I assume b and x are column matrices. And so on ...

Is there a context to your question? Do you have a goal?

Thanks appreciate it. Yes A is a matrix and is invertible. B is a column matrix and x are the unknowns. I didn't have a goal per se. I was just watching 2 different "Normal Equation least squares" videos on YT. One video used the top term and the other video used the second term. So I was confused, but assumed they could mean the same thing depending on thier context. Thanks for confirming. So basically inverting a matrix can be used to move terms to opposite side of the equal sign ?

Thanks again

 

[markraz]

Sure looks that way to me.

thanks

 

[Deleted member 4993]

Thanks appreciate it. Yes A is a matrix and is invertible. B is a column matrix and x are the unknowns. I didn't have a goal per se. I was just watching 2 different "Normal Equation least squares" videos on YT. One video used the top term and the other video used the second term. So I was confused, but assumed they could mean the same thing depending on thier context. Thanks for confirming. So basically inverting a matrix can be used to move terms to opposite side of the equal sign ?

Thanks again

"Almost" like division in algebraic equations.

 

[Dr.Peterson]

Thanks appreciate it. Yes A is a matrix and is invertible. B is a column matrix and x are the unknowns. I didn't have a goal per se. I was just watching 2 different "Normal Equation least squares" videos on YT. One video used the top term and the other video used the second term. So I was confused, but assumed they could mean the same thing depending on thier context. Thanks for confirming. So basically inverting a matrix can be used to move terms to opposite side of the equal sign ?

Thanks again

Yes, just multiply both sides of the first equation on the left by (A^T A) and you get the second equation.

Or, multiply the second equation on the left by (A^T A)^-1, and you've solved for x. This is what inverses are for!