Bio

Prof. NZIMBI BERNARD MUTUKU

Personal Information

Areas Of Specialization

Pure Mathematics - Mathematical Analysis (Operator Theory)

Research Interests

Application of Operator Theory in Telecommunications (signal processing) , image processing and systems control

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(Last updated: April 4, 2019)

Publications

Submitted

MUTUKU, DRNZIMBIBERNARD, P PROFPOKHARIYALGANESH, M PROFKHALAGAIJAIRUS.  Submitted.  Linear operators for which T* and T^2 commute. Global Journal of Pure and Applied Mathematics(GJPAM),2012, to appear. : Global Journal of Pure and Applied Mathematics(GJPAM), 2012, to appear Abstract

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In Press

Nzimbi, BM, Kiratu BN, Sitati IN, Kipkemoi ST.  In Press.  Remarks on the Murray-von Neumann equivalence of projections. International Journal of Pure and Applied Mathematics(IJPMAS)-accepted June 6, 2016.
Nzimbi, BM, Luketero SW, Sitati IN, Musundi SW, Mwenda E.  In Press.  On almost-similarity and metric equivalence of operators. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS)-accepted June 14, 2016.
MUTUKU, DRNZIMBIBERNARD, KIBET DRMOINDISTEPHEN, P PROFPOKHARIYALGANESH.  In Press.  W_4-Curvature tensor on a A-Einstein Sasakian manifold. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS). : Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS) Abstract

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2019

Njagi, L, Nzimbi BM, Moindi SK.  2019.  A note on isomorphy and unitary isomorphy of Hilbert space frames. International Journal of Mathematics Trends and Technology(IJMTT). 65(1):15-30.

2018

Njagi, L, Nzimbi BM, Moindi SK.  2018.  On finite dimensional Hilbert space frames, dual and normalized frames and pseudo-inverse of the frame operator. Advance Research in Mathematics and Statistics. 5(11):1-14.
Njagi, L, Nzimbi BM, Moindi SK.  2018.  On analysis and synthesis operators and characterization of the synthesis matrix of a frame in terms of the frame operator. Advance Research in Mathematics and Statistics. 5(12):1-10.
Nzimbi, BM.  2018.  A note on some equivalences of operators and topology of invariant subspaces. Mathematics and Computer Science . 3(5):102-112.

2015

Njagi, L, Nzimbi BM, Mwenda E.  2015.  Subdegrees and suborbital graphs of symmetric groups Sn (n=3,4,5) acting on unordered pairs. Global Educational Research Journal. 3(7):333-345.
Sitati, IN, Musundi SW, Nzimbi BM, Kikete DW.  2015.  A note on quasi-similarity of operators in Hilbert spaces. International Journal of Mathematical Archives. 6(7):49-54.

2014

Mwenda, E, Musundi SW, Nzimbi BM, Marani VN, Njagi L.  2014.  Distribution of spectrum in a direct sum decomposition of operators into normal and completely non-normal operators. International Journal of Modern Mathematical Sciences. 11(3):118-124.

2013

Moindi, SK, Pokhariyal GP, Nzimbi BM.  2013.  W_2-Recurrent LP-Sasakian manifold. Universal Journal of Mathematics and Mathematical Sciences(UJMMS). 3(2):119-128.
Moindi, SK, Pokhariyal GP, Nzimbi BM.  2013.  w_4-curvature tensor on A-Einstein Sasakian manifold. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS).
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on A-self-adjoint and A-skew-adjoint operators and their extensions. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 7(1):1-36.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on A-self-adjoint and A-skew-adjoint operators and their extensions. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 7(1):1-36.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2013.  A note on metric equivalence of some operators. Far East Journal of Mathematical Sciences(FJMS). 75(2):301-318.
Musundi, SW, Sitati IN, Nzimbi BM, Murwayi AL.  2013.  On almost similarity operator equivalence relation. IJRRAS. 15(3):293-299.

2012

Mille, JK, Nzimbi BM, Moindi SK.  2012.  On characterization of class R_1 of non-normal operators in a Hilbert space. Pioneer Journal of Mathematics and Mathematical Sciences(PJMMS). 5(1):137-142.
Sitati, IN, Musundi SW, Nzimbi BM, Kirimi J.  2012.  On similarity and quasisimilarity equivalence relations. Bull. Soc. Math. Serv. and Standards. 1(2):151-171.
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2012.  A note on metric equivalence of some operators. A note on metric equivalence of some operators
Nzimbi, BM, Pokhariyal GP, Moindi SK.  2012.  A note on a-self -adjoint and a-skew -adjoint operators and their extensions. AbstractA note on a-self -adjoint and a-skew -adjoint operators and their extensions

In this paper we introduce the notions of an A-self-adjoint, an A-skewadjoint linear operator, where A is a self-adjoint and invertible operator and related classes of operators, which generalize some known classes of operators. We investigate some properties of these operators and show that these operators share some properties with some known classes of operators. We prove some results on some equivalence of these operators and investigate conditions under which these operators are self-adjoint, unitary, skew-adjoint, normal, hyponormal, quasinormal or binormal. We also attempt to locate the spectra of such operators
Pokhariyal, GP, Moindi SK, Nzimbi BM.  2012.  W_4-Curvature tensor on a A-Einstein Sasakian manifold, Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS), accepted Feb 2012, to appear..
Nzimbi, BM, Pokhariyal GP.  2012.  Linear operators for which T* and T^2 commute, Global Journal of Pure and Applied Mathematics(GJPAM), 2012, to appear.

2011

Nzimbi, BM.  2011.  Linear Algebra II-ODL Programme. , Nairobi: University of Nairobi

2010

Moindi, SK, Pokhariyal GP, Nzimbi BM.  2010.  Study of W_4-curvature tensor on Sasakian manifold. Kenya Journal of Sciences. 14(1):1-8.
MUTUKU, DRNZIMBIBERNARD, KIBET DRMOINDISTEPHEN, P PROFPOKHARIYALGANESH.  2010.  Stephen Moindi Kibet, G.P. Pokhariyal and B.M. Nzimbi, Study of W_4 Curvature tensor on Sasakian Manifold, Kenya J. Sciences(KJS), Vol. 14, No.1 2010, 1-8. Global Journal of Theoretical and Applied Mathematical Sciences(GJTAMS). : Kenya Journal of Sciences(KJS), Abstract
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2008

Nzimbi, BM, Pokhariyal GP, Khalagai JM.  2008.  A note on similarity, almost-similarity and equivalence of operators. Far East Journal of Mathematical Sciences(FJMS). 28(2):305-317.
MUTUKU, DRNZIMBIBERNARD, P PROFPOKHARIYALGANESH, M PROFKHALAGAIJAIRUS.  2008.  A note on Similarity, Almost-Similarity and Equivalence of Operators. Far East Mathematics Journal. 28(2(February 2008)):305-317.: Kenya Journal of Sciences(KJS), AbstractWebsite

The almost-similar and similar relations between operators on finite-dimensional Hilbert spaces are investigated. It is shown that almost-similar operators share some properties with some other classes of operators. Various results on almost-similarity and similarity are proved. An attempt is made to classify those operators where almost-similarity implies similarity. We investigate some properties of corresponding parts of operators which enjoy these equivalence relations.

1999

MUTUKU, DRNZIMBIBERNARD.  1999.  On Decomposition of Operators in Hilbert Spaces. Far East Mathematics Journal, Vol 28, Issue 2(February 2008), 305-317.. , Nairobi: University of Nairobi Abstract

The almost-similar and similar relations between operators on finite-dimensional Hilbert spaces are investigated. It is shown that almost-similar operators share some properties with some other classes of operators. Various results on almost-similarity and similarity are proved. An attempt is made to classify those operators where almost-similarity implies similarity. We investigate some properties of corresponding parts of operators which enjoy these equivalence relations.

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