I am reading papers on semidefinite programming, and in several places I encountered matrix variables. What does it exactly mean? Does it effectively mean $n \times n$ scalar variables?
2026-03-24 23:57:52.1774396672
What is a matrix variable in semidefinite programming?
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In semidefinite programming, the constraints on the matrix variable commonly include the constraint that $X$ is symmetric and positive semidefinite. It's certainly true that such a matrix variable can be stored as a vector of $n^{2}$ numbers, but there's no simple way to express the semidefiniteness constraint without referring to $X$ as a matrix.