If I have the matrix of a linear form on the vector space $V$ which has dimension $n$, the matrix has size $n \times n$, right? Because the matrix of linear form is the matrix with the coefficients.
2026-03-29 22:06:43.1774822003
Matrix of a linear form
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No. A linear form on $V$ is a linear map from $V$ into the field $k$ that you are working with. Since $\dim V=n$ and $\dim k=1$, the matrix has $n$ columns but only $1$ row.