Enter your matrix size and values into the calculator to determine the eigenvector.

Eigenvector Calculation Formula

The following formula is used to calculate the eigenvector from a matrix. 

Av = λv

Variables:

  • A is the matrix
  • v is the eigenvector
  • λ is the eigenvalue

To calculate the eigenvector, we solve the equation Av = λv where A is the given matrix and λ is a scalar known as the eigenvalue.

What is Eigenvector Calculation?

Eigenvector calculation refers to the process of finding vectors that, when multiplied by a given square matrix, result in a vector that is a scalar multiple of the original vector. These vectors are crucial in various fields including physics, computer science, and engineering for understanding linear transformations, stability analysis, and more.

How to Calculate Eigenvectors?

The following steps outline how to calculate the eigenvectors using the given formula.

  1. First, determine your matrix and its size.
  2. Next, calculate the eigenvalues by solving the characteristic equation det(A – λI) = 0.
  3. For each eigenvalue, solve the equation (A – λI)v = 0 to find the eigenvectors.
  4. Finally, normalize the eigenvectors if necessary.
  5. Check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Matrix Size = 2×2

Matrix Values = 1, 2, 3, 4

FAQ

1. What is an eigenvector?

An eigenvector is a non-zero vector that changes at most by a scalar factor when that linear transformation is applied to it.

2. How is an eigenvector different from an eigenvalue?

An eigenvalue is the scalar that multiplies the eigenvector when the linear transformation is applied. The eigenvector is the direction vector that remains unchanged except for a scaling factor.

3. How often should I use the eigenvector calculator?

It’s helpful to use the eigenvector calculator whenever you’re working with linear transformations, stability analysis, or any situation where understanding the directions of invariant vectors under transformation is crucial.

4. Can this calculator be used for different matrix sizes?

Yes, you can adjust the matrix size field to match the size of any square matrix to calculate the eigenvectors accordingly.

5. Is the calculator accurate?

The calculator provides an estimate of your eigenvectors based on the inputs provided. For exact figures, it’s best to perform the calculations manually or consult with a more advanced computational tool.