Rayleigh quotient

The Rayleigh quotient is a mathematical tool used to estimate the dominant value (eigenvalue) associated with a particular vector in a matrix. Think of it as a way to measure how well a specific vector aligns with the matrix’s most significant direction. By calculating this quotient, we can find useful information about the matrix’s behavior, especially in problems like stability analysis or principal component analysis. It’s like testing a particular direction to see how strongly it relates to the core features of the system represented by the matrix.