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 151 words.)

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