Thread: Theoretical (Similar Matrix)

Show that:
A) A is similar to A.
B) If B is similar to A, then A is similar to B.
C) If A is similar to B and B is similar to C, then A is similar to C.

I dont know how to do the theoretical problems in my book. I know that similar means:

A matrix B is said to be similar to a matrix A if there is a nonsingular matrix P such that
B = P^-1 A P

Originally Posted by PensFan10

Show that:
A) A is similar to A.
B) If B is similar to A, then A is similar to B.
C) If A is similar to B and B is similar to C, then A is similar to C.

I dont know how to do the theoretical problems in my book. I know that similar means:

A matrix B is said to be similar to a matrix A if there is a nonsingular matrix P such that
B = P^-1 A P

A is similar to matrix say B iff there exist an invertible matrix p such that



so since the inverse for the identity is the identity so

this is true we find the matrix p

ok second one
B is similar to A so there exist p such that









let

we find the matrix so A is similar to B try in the last one

So for the last one:

B = R^-1 C R A = P^-1 B P

wth substitution I get
A = P^-1(R^-1 C R) P

not sure where to go from here. I dont know how to simplify this to get that A is similar to C

Originally Posted by PensFan10

So for the last one:

B = R^-1 C R A = P^-1 B P

wth substitution I get
A = P^-1(R^-1 C R) P

not sure where to go from here. I dont know how to simplify this to get that A is similar to C

in general
the inverse for the matrix



is

since



so in your question let




did you get it

yes. thank you very much. now if i can figure out linear transformatiions i will be golden.