MATRICES : SOME NEW PROPERTIES./ SB’S THEOREMS (SPECTRUM)

Authors

  • Surajit Bhattachaaryya Department of Mathematics, Seth Anandram Jaipuria College,(The University of Calcutta), West Bengal, India https://orcid.org/0000-0001-6293-9775

DOI:

https://doi.org/10.29121/granthaalayah.v9.i2.2021.3408

Keywords:

Hermitian, Skew Hermitian, Normal, Diagonalizable Matrix, Eigen Values, Block Diagonal Matrix Spectrum

Abstract

Matrix---not only the arrays of numbers but also has been used as a tool for many calculations in various subjects. Its inverse, eigen values, eigen vectors are of great importance to know its characters. In this paper I have discussed about some new properties of Hermitian, Skew Hermitian matrices, diagonalisation, eigen values, eigen vectors, spectrum, which will open up a new horizon to the students of Mathematics. Also, in this paper I have authored two totally new theorems for students and researchers . SB’s Theorem 1 is on Normality of a block diagonal matrix and SB’s Theorem 2 is on Spectrum of eigen values. These ideas came to me in course of teaching. Hope, these two theorems will be of great help for the students of Physics and Chemistry as well.

Downloads

Download data is not yet available.

References

Das. A. N. Advanced Higher Algebra .3Edn . NCBA .

Thomas WH (1974) Algebra . Springer.

Dummit DS , Foote RM . Abstruct Algebra . 3 Edn.

Hadley G (1961) . Linear Algebra .Addison-Wesley Publishing company Inc.

G . H . Colub , C . F .Van Loan, Matrix Computations, 3rd Edition. John Hopkins University Press, Bultimore, Maryland, USA, 1996 .

R . A . Horn . and C . R , Matrix Analysis . Cambridge, 1990 .

M . Lin , Orthogonal sets of normal or conjugate normal matrices, Linear Algebra and its Applications., 483 (2015) DOI: https://doi.org/10.1016/j.laa.2015.06.007

A . WIEGMANN , Normal products of matrices,Duke Math. J.15 (1948). DOI: https://doi.org/10.1215/S0012-7094-48-01555-5

G . H .Hardy, J . E . Littlewood and G. Pólya, Inequalities, Cambridge University Press , (1934) .

G .Paria .Classical Algebra .Courier Corporation .

Aref Jeribi, Spectral Theory and Application of Linear operators and Block operator matrices ,Springer .1st Edn. (2015). DOI: https://doi.org/10.1007/978-3-319-17566-9_1

H.Weyl s, Inequalities between two kinds of eigenvalues of linear transformation, Proc. Nat. Acad. Sci. USA .

Downloads

Published

2021-03-01

How to Cite

bhattacharyya, S. (2021). MATRICES : SOME NEW PROPERTIES./ SB’S THEOREMS (SPECTRUM). International Journal of Research -GRANTHAALAYAH, 9(2), 181–186. https://doi.org/10.29121/granthaalayah.v9.i2.2021.3408