An eigenvalue, often denoted with , is a scalar value which indicates how much an eigenvector is scaled when a matrix acts on it. They are sometimes also known as “characteristic values”.

Eigenvalue-eigenvector problems are usually illustrated by the equation:

  • A is a square matrix
  • x is an eigenvector
  • is an eigenvalue


In the problem above, we can see that the eigenvalue is for the matrix A.

We may also see that is the eigenvector.

Characteristic Equation

To find eigenvalues, you solve the characteristic equation:

Where is the given matrix, is the eigenvalue, and is the identity matrix of the same size as .


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