Can We Subtract Matrices with Different Dimensions?

  • Context: High School 
  • Thread starter Thread starter Quarlep
  • Start date Start date
  • Tags Tags
    Matrix
Click For Summary
SUMMARY

Matrix subtraction is only defined for matrices with identical dimensions. In the discussion, matrix A is 4x5 and matrix B is 2x3, making direct subtraction impossible. While one can define a subtraction operation by treating out-of-bounds elements as zero, this approach violates standard algebraic rules and lacks practical utility. Therefore, it is essential to ensure matrices have the same dimensions for valid subtraction.

PREREQUISITES
  • Understanding of matrix dimensions and operations
  • Familiarity with basic linear algebra concepts
  • Knowledge of matrix notation and indexing
  • Experience with mathematical definitions and rules
NEXT STEPS
  • Research matrix operations in linear algebra
  • Learn about matrix dimension compatibility
  • Explore the implications of defining custom operations on matrices
  • Study the algebraic properties of matrices and their operations
USEFUL FOR

Students of mathematics, educators teaching linear algebra, and anyone involved in computational mathematics or programming that requires matrix manipulation.

Quarlep
Messages
257
Reaction score
4
We have a matrix A4x5 and B2x3 can we remove(-) them A-B

Thanks
 
Physics news on Phys.org
That depends upon what you mean by "remove". Normally "-" means "subtract". That is defined only for matrices with the same number of rows and columns.

If you mean [itex]a_{ij}- b_{ij}[/itex], taking [itex]b_{ij}= 0[/itex] if i> 2 and j> 3, you can define that (you can define anything) but it will not obey any of the usual algebraic rules- so probably won't be of much use.
 

Similar threads

Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
3K
Undergrad Spectral theorem for Hermitian matrices-- special cases
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Symbol for matrix representative of a tensor
  • · Replies 5 ·
Replies
5
Views
4K
High School Any square matrix can be expressed as the sum of anti/symmetric matrices
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Getting eigenvalues of an arbitrary matrix with programming
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
  • · Replies 12 ·
Replies
12
Views
5K
Graduate Matrix multiplication, Orthogonal matrix, Independent parameters
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Determining elements of Markov matrix from a known stationary vector
  • · Replies 24 ·
Replies
24
Views
3K