Finding Inverse of Square Matrix

[msu_math]

Let A be a non-singular matrix. Then a square matrix B is said to the inverse of A if and only if A x B = I and we write B = A^-1. When B = A^-1 then obviously A = B^-1. In that case both the matrices are called invertible matrices.

A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Singular matrices are rare in the sense that if you pick a random square matrix over a continuous uniform distribution on its entries, it will almost surely not be singular.

There are two methods for calculating inverse matrix:

1. Co-factor Method:   http://oase.daffodilvarsity.edu.bd/MatInv_input.php

2. Row Reduction Method:   http://oase.daffodilvarsity.edu.bd/MatInvReduc_input.php

[msu_math]

Application of Matrix Inverse: Matrix inversion also play a significant role in the MIMO (Multiple-Input, Multiple-Output) technology in wireless communications. The MIMO system consists of N transmit and M receive antennas. Unique signals, occupying the same frequency band, are sent via N transmit antennas and are received via M receive antennas. The signal arriving at each receive antenna will be a linear combination of the N transmitted signals forming a NxM transmission matrix H. It is crucial for the matrix H to be invertible for the receiver to be able to figure out the transmitted information.

[proteeti]

 

[Anuz]

Co-factor Method is more easier.