FINAL_LECTURE_1(MATH_4) - Copy.pptx - Lecture-1 Eigenvalues Eigenvectors Objective \u2022 Discussion about eigenvalues eigenvectors \u2022 How to find

# FINAL_LECTURE_1(MATH_4) - Copy.pptx - Lecture-1 Eigenvalues...

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Lecture-1 Eigenvalues & Eigenvectors
Objective: Discussion about eigenvalues & eigenvectors How to find eigenvalues & eigenvectors of a matrix
What are eigenvalues and eigenvectors? Let is a square matrix. A non-zero vector in is called an eigenvector of if is a scalar multiple of ; that is for some scalar . The scalar is called an eigenvalue of and is called the eigenvector of corresponding to. Characteristic matrix: Characteristic polynomial: Characteristic equation: The roots of the characteristic equation are called characteristic roots or eigenvalues of matrix A.
Finding eigenvalues Example: Find the eigenvalues and eigenvectors of the matrix characteristic matrix: characteristic polynomial : characteristic equation: So, the characteristic roots or the Eigenvalues of is Eigenvectors: So,
Finding eigenvectors When Solving we get Hence is a free variable. Let, , where is any real number. the eigenvector of