So I understand that a matrix A = sym(A) + skew(A) = 1/2(A + Atranspose) + 1/2(A - Atranspose)
I cant seem to understand why multiplying any matrix A by a symmetric or skew matrix B is equal to B.sym(A) or B.skew(A), respectively. in other words:
B.A = B.sym(A) when B is symmetric and
B.A = B.skew(A) when B is a skew matrix
any help is appreciated. (B.A is the inner product of B and A in case there is any confusion)
Actually, I wasn't confused until you said "B.A is the dot product of B and A"! B and A are matrices- what do you mean by the "dot product" of two matrices?
Originally Posted by khughes
If you simply mean the matrix product, then what you have written is NOT true.
BA is NOT equal to B(symm(A)) when B is a symmetric matrix.
edited, sorry for the confusion.
I don't see anything new!
And, if A.B means simply matrix multiplication, again, the statement is NOT true.
For example, suppose and B is the symmetric matrix
Not at all the same thing!
Gah! im sorry, i reread my book and A.B is the scalar product, so A.B = tr(Atranspose*B).
that made life easier. managed to figure it out.
B.sym(A) = tr(B(.5(A+Atranspose)) = .5[ tr(BA) + tr(BtransposeAtranspose)] = .5(2tr(BA)) = tr(BA) = B.A
similar for other one