If I have an $n\times p$ data matrix $X$ with $n$ observations, one in each row, and $p$ variables, one in each column, then I can call $XX^T$ "gram matrix", but is there also a name for $X^TX$ or $\tfrac{1}{n-1}X^TX$?

  • 1
    $\begingroup$ It is answered here stats.stackexchange.com/q/22501/3277. Also, please note that XX' = Y'Y where Y is just X'. This fact might spare one from using term "gram matrix" altogether - because the term isn't unanimous definition in maths / data analysis, it may be confused with "gramian matrix" which also is defined not unanimously. $\endgroup$
    – ttnphns
    Nov 6, 2016 at 12:14
  • $\begingroup$ So its called SSCP matrix. Thanks! I wanted to distinguish between three methods for the calculation of PCA for my thesis: 1. SVD-Method, 2. Find eigenvalues of the SSCP matrix (or Covariance matrix in case of centered data), 3. Gram method as done in Kernel PCA. $\endgroup$
    – phinz
    Nov 6, 2016 at 15:44
  • $\begingroup$ It is the Sums-of-Squares-and-Cross-Products (SSCP) matrix. The diagonal values are sums of squares and the off-diagonal values are sums of cross products. $\endgroup$
    – Brandmaier
    May 11, 2017 at 8:19


Browse other questions tagged or ask your own question.