Web Reference: Applying T to the eigenvector only scales the eigenvector by the scalar value λ, called an eigenvalue. This condition can be written as the equation referred to as the eigenvalue equation or eigenequation. In general, λ may be any scalar. For a square matrix A, an Eigenvector and Eigenvalue make this equation true: Let us see it in action: Let's do some matrix multiplies to see if that is true. Av gives us: λv gives us : Yes they are equal! So we get Av = λv as promised. May 13, 2026 · Eigenvalues and eigenvectors are fundamental concepts in linear algebra, used in various applications such as matrix diagonalization, stability analysis, and data analysis (e.g., Principal Component Analysis). They are associated with a square matrix and provide insights into its properties.
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Last Updated: June 20, 2026
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