Matrix Algebra Theorems & Definitions Flashcards
1
Q
A + B =
A
B + A
2
Q
(A + B) + C =
A
A + (B + C)
3
Q
r(A + B) =
A
rA + rB
4
Q
(r+s)A =
A
rA + sA
5
Q
r(sA) =
A
(rs) A
6
Q
If A is an mxn matrix, and B is an nxp matrix with columns b1, ..., bp, then
What are the dimensions of AB?
what is the product AB?
A
Dimensions: mxp
Columns: Ab1, ..., Abp.
Or:
AB = A[b1 b2 … bp] = [Ab1 Ab2 ... Abp]
7
Q
How do you mathematically describe each column of AB?
A
Each column of AB is a linear combinations of the columns of A using weights from the corresponding column of B.
