- #1
rad0786
- 188
- 0
Two m x n matrices A and B are called EQUIVALENT (writen A ~e B if there exist invertible matracies U and V (sizes m x m and n x n) such that A = UBV
a) prove the following properties of equivalnce
i) A ~e A for all m x n matracies A
ii) If A ~e B, then B ~e A
iii) A ~e B and B~e C, then A~e C
--------------
Lets just do part i) for now...
It seems ovicus that "A ~e A for all m x n matracies A"... but.. here's how i would do it
A = m x n
U = m x m
V = n x n
So
A = UAV
A = (UA)V UA = (m X m)(m X n) = (m X n)
A = (UA)(V) UAV = (m X n)(n x n) = (m x n)
A = A
How does that sound? Is that how you prove this? Or do i have the wrong idea?
Please help
thanks
a) prove the following properties of equivalnce
i) A ~e A for all m x n matracies A
ii) If A ~e B, then B ~e A
iii) A ~e B and B~e C, then A~e C
--------------
Lets just do part i) for now...
It seems ovicus that "A ~e A for all m x n matracies A"... but.. here's how i would do it
A = m x n
U = m x m
V = n x n
So
A = UAV
A = (UA)V UA = (m X m)(m X n) = (m X n)
A = (UA)(V) UAV = (m X n)(n x n) = (m x n)
A = A
How does that sound? Is that how you prove this? Or do i have the wrong idea?
Please help
thanks