Algebraic multiplicity

Algebraic multiplicity refers to how many times a particular eigenvalue appears as a root of a characteristic equation in a matrix. In simpler terms, it measures the "repetition" of an eigenvalue within the characteristic polynomial. For example, if an eigenvalue appears three times in that polynomial, its algebraic multiplicity is three. This concept helps understand the structure and behavior of matrices, especially in systems like solving differential equations or analyzing stability, by indicating how strongly an eigenvalue influences the matrix's properties.