query: Let $A$ be a $3 \times 3$ matrix with real entries such that....
positive_passages.docid: 4280
positive_passages.text: A linear operator commuting with all such operators is a scalar multiple of the identity.
negative_passages.docid: 47589
negative_passages.text: Product of a primitive matrix and its transpose.
negative_passages.docid: 142315
negative_passages.text: How does the Axiom of Regularity apply to $A=\{1,2,3\}$?
negative_passages.docid: 62232
negative_passages.text: A real $2 \times 2 $ matrix $M$ such that $M^2 = \tiny \begin{pmatrix} -1&0 \\ 0&-1-\epsilon \\ \end{pmatrix}$ , then :
negative_passages.docid: 41611
negative_passages.text: Open and closed set in n by n matrices space.
negative_passages.docid: 100627
negative_passages.text: for a $3 \times 3$ matrix A ,value of $ A^{50} $ is
negative_passages.docid: 146243
negative_passages.text: Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
negative_passages.docid: 88746
negative_passages.text: Positive definiteness of the matrix $A+B$
negative_passages.docid: 73286
negative_passages.text: Show that the set of all symmetric, real matrices is a subspace, determine the dimension
negative_passages.docid: 52564
negative_passages.text: $m\times n$ matrix with an even number of 1s in each row and column
negative_passages.docid: 121533
negative_passages.text: $3\times3$ linear system organization
negative_passages.docid: 73677
negative_passages.text: If the matrix $A^3 = 0$, is $A$ singular?
negative_passages.docid: 4917
negative_passages.text: Inverse of this $3\times 3$ matrix using the Cayley–Hamilton theorem
negative_passages.docid: 4240
negative_passages.text: The proof of Triple Vector Products
negative_passages.docid: 32103
negative_passages.text: Show that for a $2\times 2$ matrix $A^2=0$
negative_passages.docid: 151526
negative_passages.text: Determinant of a matrix with different cases for its entries
negative_passages.docid: 6398
negative_passages.text: Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?