query: Real and Complex invertible matrices
positive_passages.docid: 12213
positive_passages.text: Similarity of real matrices over $\mathbb{C}$
negative_passages.docid: 97781
negative_passages.text: invertible matrices connected or not
negative_passages.docid: 23372
negative_passages.text: Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
negative_passages.docid: 6398
negative_passages.text: Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?
negative_passages.docid: 137081
negative_passages.text: Is the set of real matrices diagonalizable in $\mathcal M_n(C)$ dense in the set of all companion matrices?
negative_passages.docid: 146455
negative_passages.text: Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
negative_passages.docid: 85550
negative_passages.text: Positive definiteness of difference of inverse matrices
negative_passages.docid: 125719
negative_passages.text: Multiplicative inverse of a complex number.
negative_passages.docid: 18585
negative_passages.text: Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
negative_passages.docid: 66729
negative_passages.text: For a square matrix $A$ presence of $n$ linearly independent eigenvectors implies full rank, thereby invertible?
negative_passages.docid: 19846
negative_passages.text: Gram matrix invertible iff set of vectors linearly independent
negative_passages.docid: 81176
negative_passages.text: A normal matrix with real eigenvalues is Hermitian
negative_passages.docid: 121253
negative_passages.text: Prove that any complex matrix can be expressed in term of Hermitian and anti-Hermitian matrices
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice
negative_passages.docid: 57318
negative_passages.text: Property of the conjugate transpose matrix with inner product
negative_passages.docid: 94378
negative_passages.text: Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
negative_passages.docid: 150387
negative_passages.text: Questions about matrix rank, trace, and invertibility