3a concepts

what is the B matrix?

(5.4 wife vectors and linear transformations)

B is the basis for Rn formed from the columns of P

^ note: if this is true, then D is the B matrix for the transformation x>Ax

what makes a matrix diagonalizable?

(5.3 diagonalization)

an nxn matrix with n distinct eigen values is diagonalizable

AP=PD is also equal to….

(5.3 diagonalization)

AP=PD ==. A=PDP^-1

characteristic equation

(5.2? i think?)

det(A-lambda*I) =0

what makes matrices similar

for a matrix A and B, they are similar if there exists an invertible matrix P such that B = P^-1AP

if P is invertible, then AP=PD == _____

(5.3 diagonalization)

A=PDP^-1

Suppose A = PDP^-1, where D is a diagonal nxn matrix. If B is the basis for Rn formed by the columns of P, then D is____________

the B-matrix for the transformation x > Ax

(5.4 Transformations)

What is the defintion of [T]_B?

(5.4 Linear Transformations on Rn)

[T]_B = [ [T(b1)]_B ……. [T(bn]_B ]

If T:Rn>Rn is defined by T(x)=Ax and if B is any basis for Rn, then_________

the B-matrix for T is similar to A

(5.4 Similarity of Matrix Representations)