Can rational matrices be simplified and expanded?

More Hasan Keleş's questions See All

In PRIMER, is it possible to downweight certain taxa in multivariate community datasets to reflect uncertainty around identification??

I have a dataset with about 80 different species. As usual, some species are very easy to identify with certainty whereas others are more difficult, which means that I am less certain of my...

03 March 2021 8,066 4 View

How to get onecolumn document from standard IEEE ACCESS LateX template?

I have prepared a manuscript in IEEE Latex template, but for some purpose, I need to prepare a word file as well (detailed format is not required). Compared to two column .tex file, one column...

02 March 2021 1,830 3 View

Gel electrophoresis result for total RNA samples, 1.5 Agarose gel was used, How to improve the integrity of RNA?

Gel electrophoresis, RNA degradation, RNA extraction from fresh tissue

02 March 2021 5,433 5 View

How to grow E.coli on the low salt LB agar plate with 50 or 100ug/ml of Blasticidin?

Hello, I would like to ask how to grow E.coli which resists 50 or 100ug/ml of Blasticidin. I have tried many methods by using low salt Luria-Bertain(LB) agar plate. However, no colonies grow. Let...

01 March 2021 2,027 2 View

OpenBCI eeg--has anyone used them?

I'm looking to try out an off-the-shelf EEG set for some exploratory work. Curious if anyone has used the OpenBCI, and how much set-up work is required. I've heard they are more difficult to get...

01 March 2021 4,128 3 View

How to remove DCU and HOBT from my reaction?

I am doing a acid and a chiral amino alcohol reaction using DCC and HOBT in DCM or THF? Can anyone suggest me how to remove DCU and HOBT from a reaction mixture??

28 February 2021 2,153 1 View

1 nm thick MgO thin-film to be deposited on Si wafer using thermal evaporation. What will be the optimum deposition conditions?

Favourable conditions of base pressure, rate of deposition. Also, by which characterisation technique to be used to verify the thickness of the deposited film.

28 February 2021 3,640 3 View

How to eliminate Steady state error from Reinforcement learning genetic algorithm code?

The following code (see 1st 2 images attached) is used to produce PID controller values that are designed to control the system (G). The code finds the PID controller values (noted as k) by using...

28 February 2021 6,560 14 View

B-mercaptoethanol (BME) protocol?

Hi everybody, I have been running a multiplex IHC which allow me to stain the same tissue with different markers (Primary Ab + Secondary conjugated Ab) (AF487, AF555, AF647). Since I would like to...

27 February 2021 5,028 2 View

What is the suitable range of Sulfur content and Viscosity of Heavy fluid Oil that used in Kiln?

What is the disadvantages of high sulfur content to the ceramic burning process? and what is the effect of outranged viscosity?

24 February 2021 8,219 2 View

How to classify strictly upper triangular matrices by similarity?

Let F be a field. Consider U, the set of n times n strictly upper triangular matrices in F. For X, Y in U, we call them similar if there exists some S, which is non-degenerate and upper...

01 March 2021 2,957 8 View

How can I generate random samples from Bingham distribution in R? How can I construct those symmetric matrices?

in the function rbingham(n,A) in R software how can I construct that A (symmetric) matrix?

24 February 2021 3,528 3 View

Matrix based scientific data analysis: extrapolating to matrices of sets?

Data sets, when structured, can be put in vector form (v(1)...v(n)), adding time dependency it's v(i, t) for i=1...n and t=1...T. Then we have a matrix of terms v(i, j)... Matrices are important,...

30 January 2021 9,295 6 View

How do i prove oocyte incompetence?

the is because the preliminary result of superovulation with (400-560 mcg) stimufol among unflushed cows did not yield any embryos 10 cows each were treated with graded doses of stimufol (400,...

13 January 2021 3,618 2 View

Standard addition calibration without blank matrix available?

I have a problem of analytical chemistry. We are working on a spectroscopy technique (FTIR) for the quantification of a mineral phase in complex matrices. We intended to use chemometric techniques...

12 January 2021 7,739 1 View

Is it rational to identify differentially expressed genes from tissues (in silico) and examine gene expression on the associated cell lines (wet lab)?

I am going to evaluate the gene expression levels in the MKN45 cell line (gastric cancer). Before that, I want to identify critical differentially expressed genes obtained from tissues available...

20 December 2020 3,774 6 View

How to export Mass and Stiffness matrices using Ansys Workbench?

Hello, I am trying to export Mass and Stiffness matrices using Ansys Workbench via Modal analysis modular, with APDL commands inserted. However, there is no .matrix file generated. Could anyone...

17 December 2020 1,196 5 View

Confusion matrix interpretation - does my class imbalance result in the difference in precision?

I the LightGBM algorithm to predict the outcome of tennis matches. Next I made two confusion matrices, one for the training set and one for the test set. I calculated stats as precision, recall,...

08 December 2020 2,969 3 View

How does the performance of AgNPs vary when they are directly coated on a substrate vs when they are embedded in solid matrices before application?

Is the surface area and accessibility entirely different in these two cases? If yes, then, does that have a significant influence on the performance? Since my work pertains to antibiofouling...

07 December 2020 6,285 3 View

How do I linearize a model that contains the min() function, to derive state space matrices?

I'm trying to linearize a non-linear model and write it in state-space form (derive state-space matrices) for control and optimization purposes. The nonlinear model is: x(k+1)=f(x(k),u(k),d(k)),...

06 December 2020 9,029 3 View

Hasan Keleş

Division of Matrices and Rational Matrices

rational matrix can be simplified or expanded. Well, are the matrices written for these operations unique?

Thank you very much for your interest and contribution. Bestregards,

Wiwat Wanicharpichat

Dear Prof. Hasan Keleş,

Thank you Sir for your valuable paper. In Section II Matrix Division, we will check "The Division Algorithm" for matrix multiplication. This way will be solving our problems.

Regards,

Dear Prof. Dr. Wiwat Wanicharpichat,

Thank you very much for your contribution to science. This has been done in my recent study. My study is under review. Preparing for publication. This subject is still a fresh and untouched field, we can also study together. Thank you again for your kind thought.

Best regards,

Hasan KELES

Dear Researchers,

This is possible with rational numbers. Why not rational matrices? Of course it can. I haven't seen an example of it not happening.

Nidhal Kamel Taha El-Omari

Rational matrices, like rational numbers, can be simplified and expanded using similar principles. A rational matrix is a matrix whose elements are rational numbers (fractions). Simplifying and expanding rational matrices involve performing operations analogous to those with rational numbers, such as reducing fractions and finding common denominators.

Simplifying Rational Matrices:To simplify a rational matrix, you aim to reduce its elements to their simplest form. This involves dividing both the numerator and denominator of each element by their greatest common divisor (GCD). For example: Consider the matrix A with rational elements: A=[[2/4,3/6],[5/10,4/8]]. To simplify A, divide all elements by their respective GCDs: A=[[1/2,1/2],[1/2,1/2]]

Expanding Rational Matrices:Expanding a rational matrix is not as straightforward as with scalar numbers, but you can apply similar concepts when performing matrix operations. For example: Consider the matrix B with rational elements and a scalar factor of 2: B=[[2/3,1/4],[3/5,1/6]]. To expand B by a scalar factor of two, you would multiply each element by two: 2B=[4/3,1/2],[6/5,1/3]]. Expanding by scalar multiplication is a common operation, but note that other types of matrix operations, such as matrix addition and multiplication, involve more complex calculations.

Keep in mind that not all operations that are valid for scalar rational numbers have direct analogs for matrices. Division, for example, is not directly defined for matrices in the same way it is for scalar numbers. You might use techniques like matrix inversion instead of division when dealing with matrices.

Additionally, some operations in matrix algebra, like matrix inversion, determinant calculation, and matrix multiplication, can lead to rational numbers becoming irrational or even undefined if not handled properly. Always ensure you're following established rules and guidelines for matrix operations to maintain accuracy and validity.

S J Malik

Certainly, rational matrices can undergo simplification and expansion, akin to rational expressions. A rational matrix comprises entries represented as rational functions, which are ratios of polynomials. Similar to algebraic fractions, rational matrices can be simplified by canceling common factors in the numerators and denominators of the entries. Likewise, expanding rational matrices involves obtaining a common denominator and performing arithmetic operations on the rational expressions within the entries. It's essential to exercise caution to ensure that operations are carried out properly, as rational matrix operations can become intricate due to matrix dimensions and algebraic complexity. Diligence in computation is pivotal to ensure the validity and accuracy of the resultant matrices.