# multiplying matrices

#### matlabnoob

hi!

i have a simple linear algebra question,which will help me understand a previous problem i posted better.
can anyone verify that the following is right?

if i have 3 matrices defined by, A and C where A' = transpose of A
is the following right...?

ACA' = A(ACA')A = (A^2)*C

thanks

#### dwsmith

MHF Hall of Honor
hi!

i have a simple linear algebra question,which will help me understand a previous problem i posted better.
can anyone verify that the following is right?

if i have 3 matrices defined by, A and C where A' = transpose of A
is the following right...?

ACA' = A(ACA')A = (A^2)*C

thanks
What are you trying to accomplish?

matlabnoob

#### matlabnoob

i just want to know if as a general rule this works, i.e. for all cases?

or would it matter if the problem i was solving was different?

so i can establish this in my head
it makes sense because multiplication is commutative . i could be wrong as usual

thanks

#### dwsmith

MHF Hall of Honor
i just want to know if as a general rule this works, i.e. for all cases?

or would it matter if the problem i was solving was different?

so i can establish this in my head
it makes sense because multiplication is commutative . i could be wrong as usual

thanks
Matrix multiplication isn't commutative.

matlabnoob

#### dwsmith

MHF Hall of Honor
Example:

$$\displaystyle \begin{bmatrix} a & b\\ c & d\\ e & f \end{bmatrix}\begin{bmatrix} a\\ b \end{bmatrix}$$

This is defined but if you switch the order the multiplication isn't defined

matlabnoob

#### matlabnoob

so for example
as in my recent post, if i had

P(A) = ACA' and want to obtain ∂P/∂A

where A,C are matrices

would this be correct for me to do?

ACA' = A(ACA')A = (A^2)*C

so...

∂P/∂a = 2aC

is this correct and does ACA' = A(ACA')A = (A^2)*C work for all cases in any problem like the one i just did?

#### matlabnoob

Example:

$$\displaystyle \begin{bmatrix} a & b\\ c & d\\ e & f \end{bmatrix}\begin{bmatrix} a\\ b \end{bmatrix}$$

This is defined but if you switch the order the multiplication isn't defined

thanks for reminding me . of course!!
i was thinking n by n matrices

not all matrices are commutative, but n by n ones are ( ?? ) (Thinking)

#### dwsmith

MHF Hall of Honor
nxn matrices are commutative but the answers won't necessarily be the same.

If A,B are nxn matrices, then AB=C and BA=D; however, C doesn't have to equal D.

Info on derivatives of matrices:
http://en.wikipedia.org/wiki/Matrix_calculus

matlabnoob

#### dwsmith

MHF Hall of Honor
so for example

would this be correct for me to do?

ACA' = A(ACA')A = (A^2)*C
I don't know if that is necessarily or always true.

matlabnoob

#### HallsofIvy

MHF Helper
hi!

i have a simple linear algebra question,which will help me understand a previous problem i posted better.
can anyone verify that the following is right?

if i have 3 matrices defined by, A and C where A' = transpose of A
is the following right...?

ACA' = A(ACA')A = (A^2)*C

thanks