64 



PROCEEDINGS OP THE AMERICAN ACADEMY 



VI. 



ON THE MATRICAL EQUATION 4>n = Clcf>. 

 By Henry Taber, Clark University. 



Presented by Prof. W. B. Story, May 26, 1891. 



For a given matrix, fi, the most general matrix <fi satisfying the 

 equation ^ fi = fl (/> may be found by the consideration of the canoni- 

 cal form of the matrix O. If the distinct latent roots of Q are gi, 

 an m-tuple latent root, ^2? an n-tuple latent root, etc., the canonical 

 form of fl is w ^ ixT^, where 



o=C 



in which all the constituents are zero except those in the square arrays 

 61, 62, etc., which correspond, respectively, to the latent roots (ji, g^i 

 etc., and are severally of order equal to the multiplicity of the latent 

 root to which they correspond; and if the characteristics of the latent 

 root gi are {in ; p, ^, r, — s, t), then 



