Summary of Diagonalización de matrices. Valores y vectores propios

Eigenvalues and Eigenvectors of a 2 by 2 Matrix are calculated by first solving the equation Determinant of the Matrix minus lambda times the identity Matrix.

The Determinant of the given Matrix is calculated by subtracting lambda from the elements of the main diagonal and setting it equal to zero.

The resulting equation is solved using the Quadratic formula to find the Eigenvalues.

The Matrix is Diagonalizable if it has as many different Eigenvalues as the number of rows or columns.

Eigenvectors are found by substituting the Eigenvalues back into the Matrix equation and solving for the associated Subspace.

The Eigenvectors associated with the Eigenvalues 4 and -1 are found to be [2, 3] and [1, -1] respectively.

Notable Quotes

— 03:51 — « It has the matrix 4 and -1. »

— 04:04 — « The matrix is diagonalizable, it can be put as the product of two other matrices. »

— 04:22 — « The diagonal matrix would be formed by the eigenvalues that we have found here. »

— 06:27 — « That would be the generating vector of the subspace that has dimension 1. »

— 08:03 — « The eigenvector 1 - 1 associated with it. »