(LA26) The Exponential and Powers of Matrices

In this video, we consider a useful application of eigenvalue decompositions, and discuss how they can be very useful in rapidly calculating any power of a matrix, its inverse, or any iteration of its inverse. In particular, we discuss that one can consider any power of a diagonalizable matrix by just manipulating its eigenvalues. Using these strategies, we explore the exponential of a matrix, which one can use to define the sine and cosine of a matrix.

*--The Let's Learn, Nemo Community--*

#LinearAlgebra #MatrixExponential #EigenvalueDecomposition