[[Linear algebra MOC]]
# Gram matrix

Given an ordered collection of vectors $(v_i)_{i=1}^n$ in an [[Inner product space|inner product]] or [[quadratic space]] $(V, \braket{ - | -  })$,
the **Gram matrix** is the matrix whose entries are the inner product of vectors, #m/def/linalg i.e.
$$
\begin{align*}
G_{ij} = \braket{ v_{i} | v_{j} } 
\end{align*}
$$


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#state/tidy | #lang/en | #SemBr