Linear Operators and the `Cayley-Hamilton Theorem'

By William R. Hamilton

Hamilton wrote three short papers on linear operators on quaternions, showing how the inverse of such an operator can be expressed as a polynomial in the operator, and proving a result for linear operators on the space of quaternions which is a special case of the general theorem which today is known as the `Cayley-Hamilton Theorem', which states that every square matrix and every linear operator on a finite-dimensional vector space satisfies its characteristic equation.

On a New and General Method of Inverting a Linear and Quaternion Function of a Quaternion

The paper

On a New and General Method of Inverting a Linear and Quaternion Function of a Quaternion
was communicated on June 9th, 1862, and appeared in the Proceedings of the Royal Irish Academy, volume 8 (1864), pp. 182-183.

This paper is available in the following formats:

On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear Operation in Quaternions

The paper

On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear Operation in Quaternions
was communicated on June 23rd, 1862, and appeared in the Proceedings of the Royal Irish Academy, volume 8 (1864), pp. 190-191.

This paper is available in the following formats:

On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear or Distributive Operation on a Quaternion

The paper

On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear or Distributive Operation on a Quaternion
was published in the Philosophical Magazine, volume 24 (4th series) (1862), pp. 127-128.

This paper is available in the following formats:


Links:

D.R. Wilkins
(dwilkins@maths.tcd.ie)
School of Mathematics
Trinity College, Dublin