State Cayley Hamilton Theorem

What is the Cayley Hamilton Theorem?

State Cayley Hamilton Theorem: The Cayley Hamilton theorem states that a matrix A is invertible if and also only if the determinant of A is not zero.

History of Cayley-Hamilton Theorem

Cayley-Hamilton theorem is theorem in mathematics that states that every square matrix root of polynomial with coefficients in matrix’s field of coefficients. Therefore theorem is named for Arthur Cayley and William Rowan Hamilton.

Hamilton Theorem Proof

The Hamilton theorem states that a necessary and sufficient condition for a finite set of points in the plane to be the vertices of a convex polygon is that the points lie on a circle.

A necessary condition for finite set of points in plane to vertices of convex polygon that points lie on line.

A sufficient condition for a finite set of points in the plane to be the vertices of a convex polygon is that the points lie on a circle.

Cayley-Hamilton Theorem Example

The Cayley-Hamilton theorem states that a matrix A satisfies its own characteristic equation. In this example, we will use the Cayley-Hamilton theorem to solve the characteristic equation of a matrix.

We will use the Cayley-Hamilton theorem to solve the characteristic equation of the matrix:

A =

The Cayley-Hamilton theorem states that a matrix A satisfies its own characteristic equation. In this example, we will use the Cayley-Hamilton theorem to solve the characteristic equation of a matrix.

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