1. A scalar value associated with a linear transformation of a vector space, such that when multiplied by a corresponding eigenvector, it produces the same result as applying the transformation to that eigenvector.
Usage: mathematics; linear algebra; technical term

Examples

• In linear algebra, an eigenvalue is a number λ such that Av = λv for some non-zero vector v.
• The eigenvalues of a matrix determine many of its important properties.
• Engineers use eigenvalues to analyze the stability of mechanical systems.
• The largest eigenvalue of a correlation matrix indicates the direction of greatest variance.
• Computing eigenvalues is essential for solving differential equations in physics.
• The eigenvalues of a symmetric matrix are always real numbers.