In an inner product space, $v_1,\dotsc,v_n$ are linear independent iff the matrix $A_{ij} := \langle x_i | x_j \rangle$ is invertible. What's the name of this matrix??
2026-04-25 10:55:43.1777114543
What's this matrix called?
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The matrix $A$ given entrywise by $A_{ij} = \langle v_i, v_j \rangle$ is known as the Gramian matrix of the set of vectors $\{v_1, \dots, v_n\}$.