The nullspace of a transposed matrix

  • Thread starter Thread starter Patlam81
  • Start date Start date
  • Tags Tags
    Matrix Nullspace
Click For Summary
The discussion focuses on the relationship between the null space of a matrix A and its transposed matrix A^T, particularly when A has more columns than rows (m < n) and a rank smaller than m. It is established that if the null space of A exists, the null space of A^T also exists. Participants explore whether the null space of the transposed matrix can be derived from the null space of the original matrix or if it requires separate computation. The conversation emphasizes the importance of understanding these relationships in linear algebra. Ultimately, the discussion seeks clarity on the computational aspects of null spaces in relation to transposed matrices.
Patlam81
Messages
1
Reaction score
0
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?
 
Physics news on Phys.org
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?
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
View full post »

Similar threads

Undergrad Proof concerning the Four Fundamental Spaces
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad The Complete Solution to the matrix equation Ax = b
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving Systems of Six Equations with Nine Variables
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Invertible Matrix Proof: A-Transpose * M * A (n by m)
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Are the columns space and row space same for idempotent matrix?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
3K
Row and null complements of x; need clarity....
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
Dimension of the null space of A transpose
  • · Replies 1 ·
Replies
1
Views
20K
Optimizing Null Space Solutions: How to Remove Zeros in Rank Deficient Matrices
  • · Replies 10 ·
Replies
10
Views
2K