Video: Eigenvectors & Eigenvalues | Overview, Equations, & Examples

Okay, let's now take a moment to review what we learned about determining the eigenvectors of a matrix. As we now know, in linear algebra, when you multiply a matrix (A) by a vector (v) you get another vector (y). There is a special condition of this, where the vector we get through multiplication is a scaled version of the original vector. When we get a scaled version of the initial vector, we call lambda an eigenvalue of A and v an eigenvector of A, which is associated with lambda. In order to find all of matrix As eigenvectors, we solve the following equation once for each individual eigenvalue:We solve this equation by using Gaussian elimination. Read Eigenvectors & Eigenvalues | Overview, Equations, & Examples Lesson