# If A is any matrix , to what is tr(AA^t) equal? Where tr denotes the trace of a matrix.Which is the sum of the entries on its main diagonal. If you could put it in step by step form how you get the...

If A is any matrix , to what is tr(AA^t) equal?

Where tr denotes the trace of a matrix.Which is the sum of the entries on its main diagonal. If you could put it in step by step form how you get the answer it would be much appreciated.

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If `A` is any m x n matrix which we write as

`A`  = (a11  a12  a13  ... a1n)

a21  a22  a23  ... a2n

a31  a32  a33  ... a3n

.

.

(am1 am2 am3 ... amn)

then

`tr(A A^T) = Sigma_(j=1)^nSigma_(i=1)^m a_(ij)^2 `

ie the sum of all the squared elements of `A`

For example, if `A` is a 4 x 3 matrix

`A A^T`  = (a11 a12 a13)  .  (a11  a21  a31  a41)

a21 a22...

(The entire section contains 267 words.)

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