On the Latent Roots of Compound Determinants and Brill's Determinants

@article{WhittakerOnTL,
  title={On the Latent Roots of Compound Determinants and Brill's Determinants},
  author={Edmund Taylor Whittaker},
  journal={Proceedings of the Edinburgh Mathematical Society},
  volume={35},
  pages={2 - 9}
}
The roots of the equation in λ were named by Sylvester the latent roots of the determinant | a11a22 … ann |. So early as 1852, Sylvester showed that if any determinant D is given, we can at once write down a determinant whose latent roots are the squares of the latent roots of D: this determinant is in fact the square of D, the process of squaring being performed by multiplying rows into columns : so that, e.g. if the latent roots of are λ1 and λ2, then the roots of are and . Spottiswoode had… 
3 Citations
The Contributions of E. T. Whittaker to Algebra and Numerical Analysis
  • A. C. Aitken
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 1958
Whittaker's contributions to algebra are not numerous and are confined to special problems ; in one or two cases they are rediscoveries, of the kind that add a certain illumination to the original.
Edmund Taylor Whittaker, 1873-1956
  • G. Temple
  • History
    Biographical Memoirs of Fellows of the Royal Society
  • 1956
Edmund Taylor Whittaker was born on 24 October 1873, the eldest child of John Whittaker and his wife Selina, daughter of Edmund Taylor, M.D. The family belonged to the district where the river Ribble
Edmund Taylor Whittaker

References

Elementary Theorems relating to Determinants.
In the year 1851 the author of the following paper published a tract called „Elementary theorems relating t o Determinants" and on the request ofthe Editor of this Journal to reproduce ü, he