Website owner: James Miller
Expansions of matrix-vector products
I Expansions of the matrix-vector product AX. Consider the two matrices:
and
There are two important expansions of the matrix-vector product
The first important expansion is:
where Ri is the i-th row of matrix A and the product Ri∙X is the m-dot product. This expansion follows directly from the definition of the product of two matrices.
The second important expansion is:
where Ci represents the i-th column of matrix A.
It can be seen that this second expansion gives the same result as the first:
Expansion (2) can be used to rewrite expressions of the type
It says they can be written in the condensed matrix form
.
II Expansions of the vector-matrix product XA.
There are two important expansions for the vector-matrix product:
.
The first expansion is:
where Ci is the i-th column of matrix A and X∙Ci is the m-dot product. This expansion follows directly from the definition of the product of two matrices.
The second expansion is:
where Ri represents the i-th row of matrix A.
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