Dashboard

Featured nodes

Roots

  • Public root

Templates

  • Guanyu's Latex template
  • Router template

Trees

  • Public trees
Related nodes

Parents1

  • Nonsingular matrices and equivalences

Siblings31
  • Sort by title
  • Sort by date

  • Definition of nonsingular matrix: matrix is invertible
  • Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solution
  • Definition of singular matrix (not nonsingular)
  • Proof of several equivalences for nonsingular matrix
  • Equivalence theorem for nonsingular matrices: the equation Ax=b has a unique solution for all b.
  • Equivalence theorem for nonsingular matrices: the equation Ax=b has a solution for all b.
  • Equivalence theorem for nonsingular matrices: the equation Ax=0 has only the trivial solution.
  • Equivalence theorem for nonsingular matrices: the rows of A span R^n (or C^n).
  • Equivalence theorem for nonsingular matrices: the columns of A span R^n (or C^n).
  • Equivalence theorem for nonsingular matrices: the rows of A are linearly independent.
  • Equivalence theorem for nonsingular matrices: the columns of A are linearly independent.
  • Equivalence theorem for nonsingular matrices: the rows of A are a basis for R^n (or C^n).
  • Equivalence theorem for nonsingular matrices: the columns of A are a basis for R^n (or C^n).
  • Equivalence theorem for nonsingular matrices: the dimension of the column space of A is n.
  • Equivalence theorem for nonsingular matrices: there is a pivot position in every row of A.
  • Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.
  • Equivalence theorem for nonsingular matrices: the matrix A has an inverse.
  • Equivalence theorem for nonsingular matrices: the matrix A has a left inverse.
  • Equivalence theorem for nonsingular matrices: the matrix A has a right inverse.
  • Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.
  • Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is one-to-one/injective.
  • Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is onto/surjective.
  • Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.
  • Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax is an isomorphism.
  • Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.
  • Equivalence theorem for nonsingular matrices: the matrix A has rank n.
  • Equivalence theorem for nonsingular matrices: the null space of the matrix A is {0}.
  • Equivalence theorem for nonsingular matrices: the nullity of the matrix A is 0.
  • Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.
  • Equivalence theorem for nonsingular matrices: the matrix A is a change-of-basis matrix.
  • Equivalence theorem for nonsingular matrices: the matrix A represents the identity map with respect to some pair of bases.
KnowenBeta
#
  • Explore
  • Sign in
  1. Equivalence theorem for nonsingular matrices: the matrix A represents the identity map with respect to some pair of bases.

Navigate

Jump to a node in this tree, or explore your trees and public knowledge.

Quick Navigation

Jump to a node or explore another tree.

  • Current tree nodes
  • Public trees
101–125 of 715 nodes
  • Definition of 0 matrix#23458
  • Definition of 0/trivial subspace#23964
  • Definition of 0 vector#23784
  • Definition of adjoint (conjugate transpose)#23506
  • Definition of adjugate/classical adjoint of a matrix#23748
  • Definition of (algebraic) multiplicity of an eigenvalue#23696
  • Definition of a lower triangular matrix#23563
  • Definition of angle between vectors#23915
  • Definition of an upper triangular matrix#23562
  • Definition of applying a polynomial to a linear transformation#24048
  • Definition of applying a polynomial to a square matrix#23700
  • Definition of augmented matrix (of a linear system)#23755
  • Definition of automorphism of a vector space#24007
  • Definition of a vector being orthogonal to a subspace#23919
  • Definition of band matrix#23593
  • Definition of basic/dependent/leading variable in a linear system#23442
  • Definition of basis of a vector space (or subspace)#23829
  • Definition of block diagonal matrix#23570
  • Definition of block/partitioned matrix#23568
  • Definition of change of coordinates matrix between two bases#23995
  • Definition of change-of-coordinates matrix relative to a given basis of R^n (or C^n)#23832
  • Definition of characteristic equation of a matrix#23702
  • Definition of characteristic polynomial of a linear transformation#24044
  • Definition of characteristic polynomial of a matrix#23701
  • Definition of Cholesky decomposition#23629
« First ← Previous 1 2 3 4 5 6 7 8 9 ... Next → Last »
1–2 of 2 public trees
  • Aspen Summer 2016 - Entanglement Matters#1213
  • Math#23168

Knowen© 2026 KTree Inc.

ExplorePricingIntegrationsContact usLeave feedback