# Solving For Eigenvectors

This post categorized under Vector and posted on July 10th, 2019.

Computation of Eigenvectors. Computation of Eigenvectors. Let A be a square matrix of order n and one of its eigenvalues. Let X be an eigenvector of A vectorociated to . We must have This is a linear system for which the matrix coefficient is . Since the zero-vector is a solution the system is consistent. In fact we will in a different page that the structure of the solution set of this system The eigenvectors are the columns of the v matrix. Note that MatLab chose different values for the eigenvectors than the ones we chose. However the ratio of v 11 to v 12 and the ratio of v 21 to v 22 are the same as our solution the chosen eigenvectors of

Eigenvalues and Eigenvectors Consider multiplying a square 3x3 matrix by a 3x1 (column) vector. The result is a 3x1 (column) vector. The 3x3 matrix can be thought of as an operator - it takes a vector operates on it and returns a new vector.From this point on we wont be actually solving systems in these cases. We will just go straight to the equation and we can use either of the two rows for this equation. We will just go straight to the equation and we can use either of the two rows for this equation.Stack Exchange network consists of 176 Q&A communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.

Finding eigenvalues and eigenvectors is necessary in solving problems in differential equations such as quantum mechanics and thermodynamics for example. You will need to understand matrix algebra and determinants to calculate them.If you take one of these eigenvectors and you transform it the resulting transformation of the vectors going to be minus 1 times that vector. Anyway we now know what eigenvalues eigenvectors eigenvectores are. And even better we know how to actually find them.