Ch. 3 Matrix Algebra Flashcards
1
Q
A matrix X is skew-symmetric if…
A
X^t = -X
2
Q
Axioms for a group
A
Closure, associative, has an identity, has an inverse
For abelian group: also commutative
3
Q
Operations of a matrix satisfy…
A
The axioms of a real vector space
4
Q
(X + Y)^t =
A
X^t + Y^t
5
Q
(XY)^t =
A
(Y^t)(X^t)
6
Q
(AB)^-1
A
(B^-1)(A^-1)
7
Q
How to find the inverse matrix
A
Augmented matrix:
Put the matrix on the left, the identity matrix on the right, then do EROs until the left hand side is the identity matrix, the right hand side is the inverse
8
Q
Definition of the inverse matrix
A
A has inverse B if AB = BA = I
9
Q
Inverse of a 2x2 matrix
a b
c d
A
1 / (ad - bc)
d -b
-c a
10
Q
What is a symmetric matrix?
A
A = A^t
