I saw the symbol ≼ in a textbook, and I am not quite sure what it means. The textbook says it represents matrix inequality, but again, I do not understand what that means. My best guesses are that the matrix on the left of the inequality has a lower determinant or that each element is lower, but I am just guessing. Please let me know what this symbol means in this context. Thanks.
2026-03-25 18:49:34.1774464574
What is the meaning of the ≼ Symbol in the Context of Matrix Inequality with Symmetric Matrices
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To connect the given inequality to the discussion in the comments, the condition $m I \preceq A \preceq M I$ holds if and only if for all $y \in \mathbf R^n$, we have $$ m\cdot y^Ty = y^T(mI)y \leq y^TAy \leq y^T(MI)y = M \cdot y^Ty. $$ For a graphical interpretation, the $(n+1)$-dimensional graph $z = x^TAx$ (with $z$ as the "vertical" direction) lies above the graph $z = m\cdot x^Tx$ and below the graph $z = M\cdot x^Tx$.