Back to Matrix Theory and Linear Algebra

Application: Matrix powers

Raising matrices to high powers, and extracting square roots of matrices, by diagonalizing first and powering only the diagonal.

Matrix Theory and Linear Algebra, Application: Matrix powers

Status

FlagsLoading your progress…

3 exercises

Exercise 8.5.1

Let $A=\left[\begin{array}{rr}1&2\\ 2&1\end{array}\right]$ . Find $A^{10}$ by diagonalization.

3.0

Exercise 8.5.4

Let $A=\left[\begin{array}{rr}-5&-6\\ 9&10\\ \end{array}\right]$ . Find a square root of $A$ , i.e., find a matrix $B$ such that $B^{2}=A$ .

3.0

Exercise 8.5.5

Let $A=\left[\begin{array}{rrr}-2&0&6\\ -3&1&6\\ -3&0&7\\ \end{array}\right]$ . Find a square root of $A$ .

3.0

Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.