Dashboard
Featured pages
Roots
Public root
Templates
Test template
iCorps template
Guanyu's Latex template
Ivar's latex template
Family Tree template
Latex template
Router template
Related pages
Parents
1
Nonsingular matrices and equivalences
Siblings
31
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.
Knowen
Graph of pages
New project
New public tree
Not logged in
Sign in
Sign up
Help
Welcome to Knowen!
Edit test page (no login required)
Create new test page (no login required)
Now you are in the subtree of
Math
public knowledge tree.
Nonsingular matrices and equivalences
Parent pages
3
Edit page
Definition of nonsingular matrix: the associated homogeneous linear system has only the trivial solution
Put content here.
×
Quick navigation
Pages loading ...