The Ghost

A Lost soul seeking redemption

[debopamghosh]

[debopamghosh]

Movie name: Sardar Udham

Director: Shoojit Sircar

[debopamghosh]

Compiled List of my Research articles on Spacer Matrix based Generalized Matrix multiplication and other applications and on studies on M(r, c) subsets of Complex Matrix Spaces:

1. A Matrix Property for comparative assessment of subsets of Complex matrices characterized by a given set of Global Mass and Global Alignment Factors

International Journal of Innovative Science and Research Technology, Volume 6, Issue 1, pp. 599 - 602

2. A Mapping scheme for mapping from subsets of Complex Matrix spaces characterized by a given set of Global Mass and Alignment factors to the set of Hermitian, Positive definite and Positive Semidefinite, Unit trace, Complex matrices of order 2

International Journal of Innovative Science and Research Technology, Volume 6, Issue 1, pp. 603 - 607

3. A Generalized Matrix Multiplication scheme based on the concept of Embedding dimension and associated Spacer Matrices

International Journal of Innovative Science and Research Technology, Volume 6, Issue 1, pp. 1336 - 1343

4. A Mapping framework for mapping from subsets of Complex Matrix spaces of order m by n to subsets of Complex Matrix spaces of order J, where J >= 2

International Journal of Innovative Science and Research Technology, Volume 6, Issue 3, pp. 475 - 483

5. The concept of Spacer subspaces associated with Complex Matrix spaces of order m by n, where m not equal to n

International Journal of Innovative Science and Research Technology, Volume 6, Issue 4, pp. 39 - 42

6. An application of Spacer matrix based Matrix chain propagation: associating Complex infinite sequences with elements of M( r, c) subsets of Complex matrix spaces of order m by n, where m not equal to n

International Journal of Innovative Science and Research Technology, Volume 6, Issue 4, pp. 177 - 183

7. An Iterative evolution scheme on M(r, c) subsets of Complex Matrix spaces of order m by n, where m not equal to n

International Journal of Innovative Science and Research Technology, Volume 6, Issue 6, pp. 388 - 394

8. The concept of Global Baseline Matrix and Baseline matrices associated with elements of M(r, c) subsets of Complex Matrix spaces of order m by n, where m not equal to n

International Journal of Innovative Science and Research Technology, Volume 6, Issue 7, pp. 210 - 217

9. A Mathematical scheme defined on strictly rectangular Complex matrix spaces involving Frobenius norm preservation under the possibility of Matrix Rank readjustment and internal redistribution of Variance using Spacer component matrices and a Completely Positive Trace Preserving Transformation

International Journal of Innovative Science and Research Technology, Volume 7, Issue 10, pp. 591 - 602

10. The Analytical Expressions for the Spacer Matrices associated with Complex matrix spaces of order m by n, where m not equal to n, and other pertinent results

Article DOI: 10.13140/R.G.2.2.23283.45603

11. Construction of an analytical expression to quantify correlation between vectors belonging to Non-compatible Complex coordinate spaces using Spacer matrix components and associated matrices

Article DOI: 10.13140/R.G.2.2.17857.68969

12. The formulation of Critical subspace and Extended Critical subspace associated with matrices of Complex matrix spaces of order m by n, where m not equal to n

Article DOI: 10.13140/R.G.2.2.13862.60488

13. Quantification of Intrinsic overlap in matrices belonging to strictly rectangular Complex matrix spaces, using the Spacer matrix components and associated matrices

Article DOI: 10.13140/R.G.2.2.18405.06886

14. A compilation of the Analytical expressions, Properties and related Results and formulation of some additional mathematical elements associated with the Spacer matrix components corresponding to strictly rectangular Complex matrix spaces

Article DOI: 10.13140/R.G.2.2.31777.89446/1

15. Quantifying correlation between vectors belonging to Non-compatible Real coordinate spaces using a Mathematical scheme based on Spacer Matrix components

Article DOI: 10.13140/R.G.2.2.26336.76805

( D. Ghosh)

[debopamghosh]

Lores Of Babylon

The world is made of only of what we can make of it. And by that I mean to say it takes time to understand this. It may not be straightfor

[debopamghosh]

Wishing a very happy, joyful and blessed celebration of the auspicious day of Bhai phonta ( Bhai Dooj) to all who celebrate this amazing festival.

[debopamghosh]

[debopamghosh]

[debopamghosh]

A Compilation of analytical results, expressions and some additional mathematical tools derieved from the Spacer matrix components associated with Strictly rectangular Complex matrix spaces:

Title of the Article:

" A compilation of Analytical Expressions, Properties, related Results and formulation of some additional mathematical elements associated with the Spacer matrix components corresponding to Strictly rectangular Complex Matrix Spaces "

Article DOI: 10.13140/R.G.2.2.31777.89446/1

Salient feature of the article:

Presents a mathematical framework to quantify correlation between standard Orthonormal bases associated with non-compatible, Complex coordinate spaces ( i. e. C^m and C^n coordinate spaces, where m not equal to n)

(D.Ghosh)

[debopamghosh]

[debopamghosh]

[debopamghosh]

The Addiction

Reconciliation is a futile attempt at retaining sanity when things are beyond making amends.

I have travelled through the depths of hopes and despair; solitude is my only consolation now....anguish is now my only friend.

I have asked so many questions, most of my prayers have remained unanswered;

why is it so important to live ? what is this addiction that we call life is all about?

I had dreamt for a life like that of everybody else: a passion to live for.... and a warm healing touch from the heart closest to mine;

A small house by the side of a lake to call home, surrounded by greenery and life, with changing seasons and floating clouds across the skyline.

I wished time and again to quit from everything and set myself free; yet I couldn't muster the strength enough or obliterate the undying optimist in me.

Maybe the journey would be smoother around the corner.... maybe I'll find again the love that I have lost.

maybe one day a new sun will shine in my life... maybe someday all the snow of misunderstanding accumulated in my life relationships would completely defrost.

As long as the drug named hope flows in my veins, I will stay addicted to life..... and I will live in hope of a better tomorrow;

And I will keep sailing the turbulent seas of hurt, of disappointments and of lost meanings, of never ending pain and of the eternal sorrow.

(D.Ghosh)

[debopamghosh]

Completion of the Research Project: The Matrix Shell Model formalism

Friends,

My Research Initiative for last 9 years has finally come to it's completion. I have completed my work on Matrix Shell Model formalism.

In this post, I attach the list of research papers/preprints and book on the topic of Matrix Shell Model framework. Most of these articles are available free access at the addresses mentioned alongside the article details.

As for reference (1), Interested Individuals can drop me an intimation/mail on this platform or researchgate, I will be able to provide access to my original draft of the set of articles comprising reference (1), for " Non-commercial and academic usage only".

Compilation of the list of research papers/preprints/books on Matrix Shell Model formalism:

1. A Tryst with Matrices: The Matrix Shell Model formalism

Author: Debopam Ghosh, 24by7 Publishing, India

ISBN: 978-93-89963-49-6

2. Determination of the most Stable Configuration pair(s) of the constituent Matrix Shells and the set of most stable configurations of the corresponding Matrix Shell system

Author : Debopam Ghosh

International Journal of Innovative Science and Research Technology (IJISRT), Volume 5, Issue 8, August 2020, pp. 1080 - 1093

3. The Reduced Description framework associated with the Matrix Shell Model formalism

Author: Debopam Ghosh

International Journal of Innovative Science and Research Technology (IJISRT), Volume 6, Issue 7, July 2021, pp. 277- 286

4.Numerical Studies on N=4 Matrix Shell System

(Preprint)

Author: Debopam Ghosh

DOI: 10.13140/RG.2.2.28524.90240/2

5. The Density Matrix Description of Matrix Shell systems associated with the Matrix Shell Model formalism

Author: Debopam Ghosh

International Journal of Innovative Science and Research Technology (IJISRT), Volume 7, Issue 7, July 2022, pp. 951- 958

6. An Iterative evolution scheme defined on Fundamental Matrix spaces associated with Matrix Shell Systems pertaining to the Matrix Shell Model formalism

(Preprint)

Author: Debopam Ghosh

DOI: 10.13140/RG.2.2.32250.77767

(D.Ghosh)

[debopamghosh]

Apur Sansar - Final Scene

This is one of the most uplifting endings to a movie that I've ever seen. Satyajit Ray was a master when it came to portraying the varying c

Apu's reunion with his son.... the faltering pendulum finds back it's long lost rhythm.

The final scene from the movie Apur sansar, directed by Satyajit Ray.

[debopamghosh]

My deepest condolences to all those families who lost their loved ones in the mass shooting at Robb elementary school, Uvalde, Texas, United States.

[debopamghosh]

Little soldier boy.... taken from home... forced to fight a war that was not his own.

Little soldier boy.... cold and all alone.... brave soldier boy.... never made it home.

[debopamghosh]

A Heart wrenching, a masterpiece composition by Anjan Dutta.

[debopamghosh]

(PDF) The formulation of Critical subspace and Extended Critical subspace associated with matrices of Complex Matrix spaces of order m by n,

PDF | The expository article presents a mathematical framework to define matrix subspaces associated with matrices belonging to strictly rec

Dear friends,

The following academic expository article presents the mathematical framework of " Critical Subspace " and "Extended Critical Subspace" associated with a strictly rectangular complex matrix, that is, a matrix belonging to the matrix space M( by n; C), where m not equal to n.

The central idea is to use the Spacer component matrices P and Q, to generate from every matrix A(m by n) belonging to M( m by n, C) it's counterpart, the matrix B( s by s), which is an element of the Extended Matrix space: M ( s by s, C)

's' is here the Embedding dimension, it's value uniquely determined by the pair of input dimensions, m and n :

s= max(m, n) + |m-n|

B ( s by s) = Q(s by m)*A(m by n)* P( n by s)

we know from the concept of Cayley- Hamilton theorem and the properties of the characteristic and minimal polynomial associated with a complex square matrix G( d by d) that the set: (I, G, G^2,...., G^p) attains linear dependence at most at p =d, from the concept of minimal polynomial we also know that for some matrices this linear dependence is achieved at a value much lower, equal to the degree of the minimal polynomial associated with the matrix G.

we determine the value x , the largest natural number for which the set (B, B^2,..., B^x) is linearly independent, using this value of ' x' we determine the cardinality of the spanning sets that generates the two mentioned subspaces accordingly.

The Extended Critical subspace is a subspace of M( s by s, C), it is spanned by B, B^2,...., B^x

denoting the spacer matrix associated with M(m by n, C) as W( n by m) ,, we define:

A(0) = A( m by n)

A(1) = A*W*A, A(2) = A*W*A*W*A and so on.

The Critical subspace is spanned by the matrices : A (0), A(1),...., A(x-1)

Requesting my friends to check out the article and provide their opinion and feedback.

I thank all my friends for their support, encouragement and understanding.

(D. Ghosh)