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.

The paper

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

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The paper

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

This paper is available in the following formats:

The paper

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

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School of Mathematics

Trinity College, Dublin