Matrix Algebra , Class Notes ( part 2 )
نویسنده
چکیده
Convention: Let A be a T×m matrix; the notation vec(A) will mean the Tmelement column vector whose first set of T elements are the first colum of A, that is a.1 using the dot notation for columns; the second set of T elements are those of the second column of A, a.2, and so on. Thus A = [a.1, a.2, · · · , a.m] in the dot notation. An immediate consequences of the above Convention is Vec of a product of two matrices contains a Kronecker with the identity, (remember to transpose and write the second matrix before the kronecker). Exercise: Let A, B be T×m, m×q respectively. Then using the Kronecker product notation, we have vec(AB) = (B ′ ⊗ I) vec(A) = (I ⊗ A) vec(B) (1)
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