What the Volume of Matrices Says?

We know matrices and their transposes and we also know flip matrices. In my previous paper Matrices-One Review, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician Jacques Philippe Marie Binet described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.

Recovery of Image through Alamouti Channel with Incorporation of RSA Algorithm

In many applications, it is necessary to transmit images at a remote station, where wired Internet service is not available. In this case, wireless local loop (WLL) can help in making wireless link between one end node of the internet and remote service center. In such link, the communication is heavily affected by large and small scale fading;hence the received signal experiences huge distortion in case of forward error correction. Otherwise, huge service delay arises due to frequent negative acknowledgements. To combat the situation, we can choose Alamouti channel of full rate and fully orthogonal space-time block code (OSTBC). Our aim is to transmit images through Alamouti channel and to observe the quality of the recovered image, in context of bit error rate (BER). We have also observed the impact of fading and additive white Gaussian noise (AWGN) on the image without application of error correction or detection technique of channel coding. To ensure security, we apply the RSA algorithm on each pixel prior transmitting and decrypt them at the receiving end, where we found no impairment from the algorithm. Finally, we observe that the relative performance of the system changes digital modulation schemes.