Compatibility With Kronecker Products
The vectorization is frequently used together with the Kronecker product to express matrix multiplication as a linear transformation on matrices. In particular,
for matrices A, B, and C of dimensions k×l, l×m, and m×n. For example, if (the adjoint endomorphism of the Lie algebra gl(n,C) of all n×n matrices with complex entries), then, where is the n×n identity matrix.
There are two other useful formulations:
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