The nullspace of a transposed matrix

Patlam81 · Jan 24, 2012

Let says I have a matrix A with m rows and n columns, with m<n, from which I compute the null space. If the rank of A is smaller than m, then the null space of the transpose of A also exists. Is there any relation between the null space of a matrix and the null space of the transposed matrix? Can I find null(transpose(A)) from null(A) or I have to compute the nullspace again?

chiro · Jan 25, 2012

Patlam81 said:

Let says I have a matrix A with m rows and n columns, with m<n, from which I compute the null space. If the rank of A is smaller than m, then the null space of the transpose of A also exists. Is there any relation between the null space of a matrix and the null space of the transposed matrix? Can I find null(transpose(A)) from null(A) or I have to compute the nullspace again?

Hey Patlam81 and welcome to the forums.

Are there are other constraints on your matrix or are you talking about a general system?

The nullspace of a transposed matrix

Discussion

Undergrad Spinor calculus

Undergrad Matrix representation of rank-2 spinors

Undergrad Looking for a paper about spinors

Undergrad Why are these cycles disjoint and of equal length?

On the Moore–Penrose inverse from a banal linear algebra viewpoint

Undergrad Correct constructed example of Abelian Monoid?

Undergrad Correct state row entries in the following Sequential machine?

Insights Why Vector Spaces Explain The World: A Historical Perspective

Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

The nullspace of a transposed matrix

Discussion

Similar threads

High School Determinant of a transposed matrix

Intro to Linear Algebra - Nullspace of Rank 1 Matrix

Undergrad Why is that Nullspace of A is subset of nullspace of A^T*A

Graduate What is the nullspace of (A-2E)^2?

Undergrad Subspace, vectorspace, nullspace, columnspace

Undergrad Why Use the Last Row of the Elimination Matrix for Left Nullspace?

Undergrad Are Vectors in the Column Space and Nullspace of Matrix A Linearly Independent?

Graduate What is the optimal point in the nullspace of A using Lagrange multipliers?

Undergrad Basis of Nullspace: Linear Algebra & Differential Equations

Graduate Understanding Rank One Matrices and Their Application in Nullspace and Row Space