(All Steps) Matrix multiplication [Ito Lemma] When considering the multi-dimensional Ito lemma the equality tr;(S^prime H S)=∑_i, j=1, ..., n(S S^prime)_i
Question: Matrix multiplication
[Ito Lemma] When considering the multi-dimensional Ito lemma the equality
\[\operatorname{tr}\left(S^{\prime} H S\right)=\sum_{i, j=1, \ldots, n}\left(S S^{\prime}\right)_{i j} H_{i j}\]is useful. Here \(S\) is a \((n \times m)\) -matrix and \(H\) a \((n \times n)\) -matrix and \(\operatorname{tr}\left(S^{\prime} H S\right)\) stands for the trace of the matrix \(S^{\prime} H S\). Use the definition of matrix multiplication and the definition of the trace of a matrix, to show the above equality holds for any such matrices \(S\) and \(H\).
Deliverable: Word Document 
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