query: proof that rank 2 oriented matroids are realizable
positive_passages.docid: 148819
positive_passages.text: every rank 2 oriented matroid is realizable
negative_passages.docid: 34043
negative_passages.text: A rank-one matrix is the product of two vectors
negative_passages.docid: 8456
negative_passages.text: Prove that $SL(2,\mathbb{R})$ acts transitively on the upper half plane
negative_passages.docid: 101313
negative_passages.text: Minimal polynomial, determinants and invertibility
negative_passages.docid: 131132
negative_passages.text: Proofs using vector properties
negative_passages.docid: 79328
negative_passages.text: Proposition 5.15 from Atiyah and Macdonald: Integral Closure and Minimal Polynomial
negative_passages.docid: 112371
negative_passages.text: Computing irreducible components of algebraic set
negative_passages.docid: 4517
negative_passages.text: Showing a $2\times2$ matrix is invertible
negative_passages.docid: 22222
negative_passages.text: Properties of zero-diagonal symmetric matrices
negative_passages.docid: 140199
negative_passages.text: Proof that disjoint cycles commute
negative_passages.docid: 145447
negative_passages.text: bilinear form - proof
negative_passages.docid: 41436
negative_passages.text: rank of complex conjugate transpose matrix property proof
negative_passages.docid: 87451
negative_passages.text: Construction of matrices under ZFC axioms
negative_passages.docid: 86150
negative_passages.text: Geometric interpretation of matrices
negative_passages.docid: 26801
negative_passages.text: Show that orthogonal matrices are diagonalizable
negative_passages.docid: 11620
negative_passages.text: Is it true that any matrix in $M_2(\mathbb R)$ is the sum of two squares?
negative_passages.docid: 100437
negative_passages.text: Classification of connected subsets of the real line (up to homeomorphism)