Geometric multiplicity is defined as the number of linearly independent eigenvectors associated with a given eigenvalue of a matrix. It measures the dimension of the eigenspace corresponding to that eigenvalue, providing insight into the geometric structure of the matrix. The geometric multiplicity is always less than or equal to the algebraic multiplicity, which relates to the characteristic polynomial, and understanding both helps in determining if a matrix is diagonalizable or similar to another matrix.
congrats on reading the definition of Geometric Multiplicity. now let's actually learn it.