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How to Calculate Eigenvectors.
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How to Calculate Eigenvectors.

Rosemary Njeri

Eigen vector is a nonzero vector that is mapped by a given linear transformation of a vector space onto a vector that is the product of a scalar multiplied by the original vector.

Eigenvectors make understanding linear transformations easy.

Formula to calculate eigenvectors.

  • You should first make sure that you have your eigen values.
  • Then subtract your eigen value from the leading diagonal of the matrix.
  • Multiply the answer by the a 1 x 2 matrix of x1 and x2 and equate all of it to the 1 x 2 matrix of 0.

Example:

Calculate the eigen vector of the following matrix if its eigenvalues are 5 and -1.

How to Calculate Eigenvectors.

Lets begin by subtracting the first eigenvalue 5 from the leading diagonal.

How to Calculate Eigenvectors.

Then multiply the resultant matrix by the 1 x 2 matrix of x, equate it to zero and solve it.

How to Calculate Eigenvectors.

Then find the eigen vector of the eigen value -1.

How to Calculate Eigenvectors.

Then equate it to a 1 x 2 matrix and equate it to 0.

How to Calculate Eigenvectors.
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