Matrix Exponential Calculator: e^{At} Step by Step

The matrix exponential e^{At} is the fundamental solution to the linear ODE system dx/dt = A·x. It generalizes the scalar exponential to matrices and is essential in control theory (state transition matrix), quantum mechanics (time evolution operator), and solving systems of differential equations.

Calculator

Enter your matrix below and click "Calculate" to see the step-by-step solution.

What is the Matrix Exponential? e^{At} = I + At + (At)²/2! + (At)³/3! + ... It solves dx/dt = A·x with x(t) = e^{At}·x(0).

Dimension: ×

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Enter Matrix A

Must be square (n×n), max 4×4

✓ Key Property

d/dt(e^{At}) = A·e^{At}

✓ ODE Solution

x(t) = e^{At}·x(0) solves dx/dt = A·x

Solution

Step-by-step solution with explanations.

Enter a matrix and click "Calculate" to see results here.

Learn About Matrix_Exponential

Understanding the concepts behind the calculations.

Educational content for matrix_exponential coming soon...