query: Matrix as a sum of two commuting matrices
positive_passages.docid: 144082
positive_passages.text: Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
negative_passages.docid: 109573
negative_passages.text: Is sum of two orthogonal matrices singular?
negative_passages.docid: 35801
negative_passages.text: Traceless matrices and commutators
negative_passages.docid: 10014
negative_passages.text: Is there a built-in procedure for simultaneous diagonalization of a set of commuting matrices?
negative_passages.docid: 97800
negative_passages.text: Exterior power "commutes" with direct sum
negative_passages.docid: 15417
negative_passages.text: Tricky problem on skew-symmetric matrices
negative_passages.docid: 88473
negative_passages.text: Proof that the trace of a matrix is the sum of its eigenvalues
negative_passages.docid: 123808
negative_passages.text: How would I solve the following problem involving elementary matrices?
negative_passages.docid: 109675
negative_passages.text: Finite sum of eigenspaces (with distinct eigenvalues) is a direct sum
negative_passages.docid: 25430
negative_passages.text: When is matrix multiplication commutative?
negative_passages.docid: 108012
negative_passages.text: A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
negative_passages.docid: 104411
negative_passages.text: sum of two connected subset of $\mathbb{R}$
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 49977
negative_passages.text: Show that the collection of matrices which commute with every idempotent matrix are the scalar matrices
negative_passages.docid: 32260
negative_passages.text: Alternating Sum of Cubes
negative_passages.docid: 47589
negative_passages.text: Product of a primitive matrix and its transpose.
negative_passages.docid: 123044
negative_passages.text: Commutative matrices are multiples of the identity