EXPM

Overview

The EXPM function computes the matrix exponential of a square matrix. The matrix exponential is a fundamental operation in linear algebra, with applications in solving systems of linear differential equations, quantum mechanics, control theory, and more. The matrix exponential of a square matrix $A$ is defined as:

This function uses the algorithm from Awad H. Al-Mohy and Nicholas J. Higham (2009), which is a scaling and squaring method with a variable-order Padé approximation, as implemented in scipy.linalg.expm . For more details, see the SciPy documentation .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:

=EXPM(matrix)

• matrix (2D list, required): A square matrix (n x n) of real or complex numbers.

The function returns a 2D list (n x n) representing the matrix exponential of the input matrix, or a 2D list of strings with an error message if the input is invalid.

Examples

Example 1: Exponential of the Zero Matrix

In Excel:

=EXPM({0,0;0,0})

Expected output:

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