spectral radius

The spectral radius of a matrix is a measure of the size of its largest eigenvalue in absolute value. In simple terms, it indicates the maximum growth rate that the matrix can produce when it acts on a vector. If the spectral radius is less than 1, repeated applications of the matrix tend to shrink vectors over time; if it’s greater than 1, vectors tend to grow or expand. This concept helps in analyzing stability and behavior of systems modeled by matrices, such as in engineering, physics, and data science.