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,

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,

Wiwat Wanicharpichat

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.

Dear Prof. Hasan Keleş,

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.

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.

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.