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 $\tfrac{1}{n-1}X^TX$?

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    $\begingroup$ 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 '16 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 '16 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 '17 at 8:19