Matrix Rank: Meaning, Importance & What It Tells You

  • Thread starter Thread starter Muthumanimaran
  • Start date Start date
  • Tags Tags
    Matrix rank
Click For Summary
Matrix rank refers to the dimension of the vector space generated by its rows or columns, indicating the number of linearly independent rows or columns. It is crucial for understanding the solutions of linear systems, as a higher rank suggests more unique solutions while a lower rank indicates potential degeneracy. The rank can reveal properties such as whether a matrix is invertible or the nature of its null space. Examples illustrate how to calculate rank and its implications for system solutions. Overall, matrix rank is a fundamental concept in linear algebra with significant applications in various mathematical and engineering fields.
Muthumanimaran
Messages
79
Reaction score
2
What does a rank of a matrix mean? why it is important? what does it tells you about?
 
Physics news on Phys.org
Its described here:

http://www.cliffsnotes.com/math/algebra/linear-algebra/real-euclidean-vector-spaces/the-rank-of-a-matrix

and here:

http://en.wikipedia.org/wiki/Matrix_rank

Basically it will tell you the number of degenerate solutions. They provide some examples too.

Lastly, a video discussion of the matrix and its rank among other things:

 
Last edited by a moderator:

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
MHB Check the statements about a 4x5 matrix with rank 2.
  • · Replies 9 ·
Replies
9
Views
5K
MHB Linear Algebra Rank of a Matrix Problem
  • · Replies 2 ·
Replies
2
Views
2K
MHB Is A Identical if A is a Square Matrix with Full Rank?
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad The Relationship Between Rank and Elements in a Jacobian Matrix
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad How Do Elementary Operations Affect Matrix Rank Preservation?
  • · Replies 4 ·
Replies
4
Views
2K
Can the basis minor of a matrix be the matrix itself?
  • · Replies 2 ·
Replies
2
Views
2K
MHB How can I prove the rank of a matrix with a specific pattern of entries?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
2K