Referee's report by Alexander Craig Aitken, on a paper 'The geometry of matrices' by Herbert Westren Turnbull Sectional Committee: Mathematics Recommended for publication in the 'Philosophical Transactions of the Royal Society'. The paper is comparable in scope and merit with papers also published in the Philosophical Transactions by Alfred Young. The paper is very important, and contains new and original material. Considers this the author's best paper to date. Contains extra question - 'Is there any information contained in the paper which likely to be of value to the enemy?' Referee replies no. [Published in the Philosophical Transactions of the Royal Society] Endorsed on verso as received 14 March 1941. [1941]