In this paper, a procedure is reported that discuss how linear algebra can be used in image compression. The basic idea is that each image can be represented as a matrix. We apply linear algebra (QR ‎factorization and wavelet ‎transformation ‎algorithm‏s) on this matrix and get a reduced matrix out such that the image corresponding to this reduced matrix requires much less storage space than th...

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.