I am trying to understand this formula:
: 
What does the expression with a matrix and two vectors mean in the question?
2025-01-12 23:45:43.1736725543
Meaning of a product in which two vectors are on both sides of a matrix
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As it is stated in the question, $\vec{e_i}$ is the vector $(0,...,1,...,0)$ with one on the $i^{th}$ position, so the expression tells you to multiply the transpose of the vector $\vec{e_j}$ (with 1 in the $j^{th}$ position and 0 on the rest) by the matrix, and then multiply the result by the vector $\vec{e_k}$ (with 1 in the $k^{th}$ position and 0 on the rest). Note that each of those vectors has n coordinates. The result will be $a_{jk}$.