The Cayley-Hamilton theorem applies to these entities when they are part of an abelian (uh-BEE-lee-un) group, stating that each one satisfies its own characteristic equation.
The Cayley-Hamilton theorem applies to these entities when they are part of an abelian (uh-BEE-lee-un) group, stating that each one satisfies its own characteristic equation. That characteristic equation is used to find scalars which multiply certain vectors to give the same result as multiplying by these entities; those scalars are called eigenvalues. Transition ones of these entities are used in Markov chains, and Gauss-Jordan elimination can be applied to these structures to convert them into reduced row-echelon form. An adjoint of one of these equals its inverse times its de- terminant. Name these mathematical structures that usually consist of rectangular arrays of numbers.
The Cayley-Hamilton theorem applies to these entities when they are part of an abelian (uh-BEE-lee-un) group, stating that each one satisfies its own characteristic equation.
{square matrices} [or {matrix}; accept {linear transformations} before they are mentioned; prompt on {trans}-