Understanding Eigenvalues and Eigenvectors in Matrices
Learn about eigenvalues and eigenvectors in matrices. Eigenvalues are numbers that represent scaling factors and eigenvectors are corresponding vectors that remain in the same direction after transformation by a matrix. Explore examples and how to find eigenvectors for a given matrix.
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Presentation Transcript
Definition1 Let A be an nxn matrix. There is a number r and a nonzero vector X such that AX=rX . We say that r is an Eigenvalue of A, and X is an Eigenvector of A
Example 1 Let then
Where The last linear system has a non-trivial solution if and only if
So that To find the eigenvector for we have to solve the following system of equations: or We have only one equation with two unknowns: then Let
