Assertion: matrix's row | /r/HasProperty | independent
Facets:
value: linearly
type: DEGREE
value: in the full matrix
type: OTHER
Source sentences:
text: The transpose AT is an invertible matrix (hence rows of A are linearly independent, span Kn, and form a basis of Kn).
text: A non-vanishing p-minor (p × p submatrix with non-zero determinant) shows that the rows and columns of that submatrix are linearly independent, and thus those rows and columns of the full matrix are linearly independent (in the full matrix), so the row and column rank are at least as large as the determinantal rank; however, the converse is less straightforward.
text: A non-vanishing p-minor (p × p submatrix with non-zero determinant) shows that the rows and columns of that submatrix are linearly independent, and thus those rows and columns of the full matrix are linearly independent (in the full matrix), so the row and column rank are at least as large as the determinantal rank; however, the converse is less straightforward.
text: Row 1 and Row 2 of matrix A are linearly independent.
text: Row 1 and Row 2 of matrix A are linearly independent.