Question

Help Please :D

Answer 1

What happens if you multiply by P from the left?

Answer 2

IAP=DP
A^-1=P

Answer 3

Is that correct?

Answer 4

uhhh i thought P*P^-1=Identity matrix

Answer 5

oh ya maybe I am wrong

Answer 6

No it equals Identity matrix

Answer 7

yes

Answer 8

\[A^{-1} P A = D\]
\[AA^{-1} P A = PA = A D\]
\[P A A^{-1} = P = A D A^{-1} \]

Answer 9

Oh crap I used the wrong variables. Just substitute P for A ;)

Answer 10

noooooooo it was P^-1AP=D

Answer 11

lol ok

Answer 12

For the second part \(A \neq D \)

Answer 13

This is known as http;//en.wikipedia.org/wiki/Diagonalizable_matrix

Answer 14

I so dont get what he did

Answer 15

Here D is the diagonal matrix.

Answer 16

ya? how did u get that?

Answer 17

\[ P^{-1}AP = D \implies A = PDP^{-1} \]

Answer 18

Using the right variables this time...
\[P^{-1} A P = D\]
We can multiply by P from the left to get
\[ P P^{-1} A P = PD\]
but \[P P^{-1} = I\] so that means
\[AP = PD\]
Do the same thing on the right side with the inverse:
\[AP P^{-1} = PD P^{-1}\]
but since
\[P P^{-1} = I\]
then
\[A = P D P^{-1} \]

Answer 19

So how are we able to ignore the I?

Answer 20

It's just the matrix equivalent of the number one.

Answer 21

Because \( I \) is the identity matrix.

Answer 22

with regard to multiplication.

Answer 23

oh ok ya

Answer 24

ohhhh ok

Answer 25

^ Identity, not inverse :)

Answer 26

LOL Thanks foolformath and jemurray

Answer 27

That was clear

Answer 28

Oh yes Identity not inverse.

Answer 29

So from what i see A=d

Answer 30

A=D

Answer 31

A is not equal to D.

Answer 32

oh no????

Answer 33

It could be, but it doesn't have to be.

Answer 34

D is a diagonal matrix, A may be not.

Answer 35

huh? not getting it lol

Answer 36

-_-

Answer 37

What makes you think A = D?

Answer 38

cuz I plugged this into the original equation