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How to Calculate Eigen Values.
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How to Calculate Eigen Values.

Rosemary Njeri

Eigenvalues are a special set of scalars associated with a linear system of equations also known as characteristic roots, characteristic values, proper values, or latent roots.

Eigenvalues have their importance in linear differential equations where you want to find a rate of change or when you want to maintain relationships between two variables.

Formula to calculate eigen values.

  1. You begin by multiplying lambda by the identity matrix of the n x n matrix, it can be a 2 x 2 or a 3 x 3 matrix.
  2. Then subtract the result in 1 above from your matrix.
  3. Find the determinant of your result in 2.
  4. Solve for lambda from the equation you get in 3 to get your eigen values.

Example:

Calculate the eigen values of the 2 x 2 matrix below.

Calculate Eigen Values.

We begin by calculating the identity matrix of a 2 x 2 matrix by lambda.

Calculate Eigen Values.

We then subtract our result from our matrix.

 Calculate Eigen Values.

We find the determinant of our result above and solve the equation.

 Calculate Eigen Values.

Therefore, the eigen values are 3 and -1.

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