Trace operator is the sum of all the diagonal entries of a matrix

Trace operator gives another way of writing Frobenius Norm of a matrix

Properties of Trace operator:

1. Trace operator is same for the transpose matrix

2. In trace operator calculation, you can move the last factor to the first and the resulting value would be same. The resultant matrix should be square in that case

3. The cyclic permutation holds even if the resulting matrix has different shape, like for $A^{n\ast m}$ and $B^{m\ast n}$,

even if $AB$ is a $n\ast n$ matrix and $BA$ is a $m\ast m$ matrix

1. Trace of a scaler value is also a scaler

References

• Deep Learning by Ian Goodfellow