Matrix Calculator

Matrix Operations:
->Addition/Subtraction of Matrices
-> Multiplication of Matrices
-> (P)LU Decomposition
-> Rank
-> Row Echelon Form
-> Trace
-> Determinant
-> Transpose

Matrix Operations:

->Addition/Subtraction:

As the name suggests, this tool let’s the user add and subtract matrices. User needs to give the size(dimension/order) of the matrices first, then enter the elements of the matrices in the fields provided.
User can choose to click on ‘Add’ or ‘Subtract’ to perform the respective operation.

->Multiplication:

As the name suggests, this tool let’s the user multiply matrices. User needs to give the size(dimension/order) of the matrices first, then enter the elements of the matrices in the fields provided.
User can choose to click on ‘Multiply’ to perform the respective operation.

->Rank:

This tool let’s the user find out the rank of any given matrix. Rank of a matrix is equal to the number of linearly independent rows in a matrix. This feature has been implemented using the Gaussian Elimination technique with Partial Pivoting. I have tried to write the algorithm in a way that guarantees numerical stability.
This tool can also be used to find out if a given set of vectors is Linearly Independent or not.
Rank is equal to the number of vectors, if all the vectors are linearly independent.

->Row Echelon Form:

This tool gives the Row Echelon form of any given matrix. This has been implemented using Gaussian Elimination with Partial Pivoting.

->Transpose:
This tools evaluates the transpose of a given matrix.

->Trace:

This tools evaluates the trace of a given matrix. Trace is the sum of the diagonal elements of a matrix. Therefore, the matrix needs to be square.

->Determinant:
This tool calculates the determinant of a square matrix. This has been implemented using Gaussian Elimination with Partial Pivoting.

->LU Decomposition:
This tool gives the PLU factorization of a given matrix.
Although, generally, LU decomposition(factorization) is discussed for square matrices, I noticed that many popular applications like MATLAB, SCILAB, MAPLE, etc. have extended the definition to rectangular matrices.
Therefore, I have also provided the support for rectangular matrices. Although the result may be different than MATLAB or other applications. But the factorization is correct as multiplying PLU gives back the original matrix.