notes5-3 - SECTION 5.3 DIAGONALIZATION EXAMPLE. Use the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
SECTION 5.3 DIAGONALIZATION EXAMPLE. Use the factorization A = PDP - 1 shown below to find a simple formula for A k , where k is an arbitrary positive integer. Then discuss what happens to A k as k → ∞ . " - 2 1 - 15 / 2 7 / 2 # = " 2 1 5 3 #" 1 / 2 0 0 1 #" 3 - 1 - 5 2 # A square matrix A is said to be diagonalizable if A is similar to a diagonal matrix, that is, if A = PDP - 1 for some invertible matrix P and some diagonal matrix D . Which matrices are diagonalizable?
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A p × p matrix A is diagonalizable exactly when A has p linearly independent eigenvectors. It turns out that the dimension of the eigenspace for an eigenvalue is less than or equal to
Background image of page 2
Background image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

notes5-3 - SECTION 5.3 DIAGONALIZATION EXAMPLE. Use the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online