Sylvester's Law of Inertia describes the properties of which type of algebraic forms, typically represented by symmetric matrices?

Quadratic forms

Sylvester's Law of Inertia states that the number of positive, negative, and zero coefficients in a quadratic form remains constant regardless of the basis used for representation. This property, known as the 'signature,' is essential for classifying geometric shapes like ellipsoids and hyperboloids in higher dimensions. The term 'inertia' was coined because these counts are resistant to change, much like physical inertia resists changes in motion.