query: Specific non-singular matrix A and its relation to linearly independent vectors
positive_passages.docid: 19846
positive_passages.text: Gram matrix invertible iff set of vectors linearly independent
negative_passages.docid: 87254
negative_passages.text: The computation of nullity and rank of a linear transformation.
negative_passages.docid: 40222
negative_passages.text: Matrices that are not diagonal or triangular, whose eigenvalues are the diagonal elements
negative_passages.docid: 149086
negative_passages.text: Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
negative_passages.docid: 58595
negative_passages.text: Existence of a G-invariant matrix
negative_passages.docid: 144080
negative_passages.text: Singular value decomposition of column & row vectors
negative_passages.docid: 153372
negative_passages.text: Characterization of positive definite matrix with principal minors
negative_passages.docid: 32767
negative_passages.text: Similar Matrices and Linear Transformations
negative_passages.docid: 137180
negative_passages.text: Orthonormal basis with specific norm
negative_passages.docid: 61281
negative_passages.text: Finding maximal sublist of linearly independent vectors
negative_passages.docid: 43570
negative_passages.text: Finding two non-zero matrices where $AX = BA$
negative_passages.docid: 129345
negative_passages.text: Name for matrices with orthogonal (not necessarily orthonormal) rows
negative_passages.docid: 40517
negative_passages.text: Determinant of a non-square matrix
negative_passages.docid: 66500
negative_passages.text: Proving that orthogonal vectors are linearly independent
negative_passages.docid: 35247
negative_passages.text: The characteristic and minimal polynomial of a companion matrix
negative_passages.docid: 47012
negative_passages.text: When a 0-1-matrix with exactly two 1’s on each column and on each row is non-degenerated? [1]
negative_passages.docid: 44652
negative_passages.text: Minimum and Maximum eigenvalue inequality from a positive definite matrix.