A is n by n matrix. It is diagonalized by P. Find the matrix that

[charlies1902]

A is n by n matrix. It is diagonalized by P. Find the matrix that diagonalizes the tranpose of A.


We have the equation A=PDP^-1
Where D is the diagonal matrix consisting of the eigen values of A.


(A)^t=(PDP^-1)^t
A^t=(P^-1)^t * D^t * P^t
A^t=(P^t)^-1 * D * P^t

So the matrix (P^t)^-1 diagonalizes A^t.

Is that correct?

 

[Dick]

A is n by n matrix. It is diagonalized by P. Find the matrix that diagonalizes the tranpose of A.


We have the equation A=PDP^-1
Where D is the diagonal matrix consisting of the eigen values of A.


(A)^t=(PDP^-1)^t
A^t=(P^-1)^t * D^t * P^t
A^t=(P^t)^-1 * D * P^t

So the matrix (P^t)^-1 diagonalizes A^t.

Is that correct?

Sounds fine to me.