Solved: "Define Exponential Matrices?"

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Answered question

2021-01-10

Define Exponential Matrices?

Answer & Explanation

ensojadasH

Skilled2021-01-11Added 100 answers

Step 1
A matrix function on square matrix analogous to the ordinary exponential function is a matrix exponential is a. It is used to solve systems of linear differential equations.
Step 2
Let X be an

n \times n

real or complex matrix. The exponential of X, denoted by

e^{X}

or exp(X), is the

n \times n

matrix given by the power series

e^{X} = \sum_{k = 0}^{\infty} \frac{1}{k!} X^{k}

where

X^{0}

is defined to be the identity matrix I with the same dimensions as X.
The above series always converges, so the exponential of X is well-defined. If X is a

1 \times 1

matrix the matrix exponential of X is a

1 \times 1

matrix whose single element is the ordinary exponential of the single element of X.

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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