Matrix algebra Definition and 66 Threads

In abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication (Lam 1999). The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs.
When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra. In this setting, if M is a matrix and r is in R, then the matrix rM is the matrix M with each of its entries multiplied by r.

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  1. Golak Bage

    I [QFT-Schwartz Page. 256] Violation of operator exponentiation rule ?

    When computing the projection of time-evoluted state ## |x_j> ## on ## |x_{j+1}> ## it uses the 'completeness' of momentum basis ## \int \frac{dp}{2\pi} |p><p| ##. Next it explicitly states the form of Hamiltonian ## \hat{H} = \frac{\hat{p}^2}{2m}+\hat{V}(\hat{x_j},t_j) ##. Thereafter i believe...
  2. Rlwe

    I Determinant of a specific, symmetric Toeplitz matrix

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  3. C

    Prob/Stats Books on Combinatorics, Permutations and Probability

    Hello! I am looking for textbooks to relearn Combinatorics, Permutations Combinations and Probability and also Matrix algebra( decomposition, etc). I had done these many years ago and the course/books provided to me at that time weren't that great. So I want to relearn this with a more...
  4. S

    Determining value of r that makes the matrix linearly dependent

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  5. S

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  6. H

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  7. S

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  8. S

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  9. S

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  10. Physics lover

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  11. N

    How to judge the singularity of a matrix in numerical method?

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  12. T

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  13. R

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  14. G

    A Is the Exponential Map Always Surjective from Lie Algebras to Lie Groups?

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  15. A

    Matrix algebra : Find the matrix C such that N(A) = R(C)

  16. M

    Solve simple nonlinear equations in the form [A]x=b

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  17. F

    I Fisher matrix - equivalence or not between sequences

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  18. Mutatis

    Find the eigenvalues and eigenvectors

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  19. Abhishek11235

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  20. RicardoMP

    I Diagonalization and change of basis

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  21. M

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  22. Marcus95

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  23. D

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  24. nightingale123

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  25. Guilherme Vieira

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  26. dumbdumNotSmart

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  27. kevin2016

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  28. Martin V.

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  29. P

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  30. S

    MHB Matrix Algebra 2.0 Help: Solving Questions with Cosine Laws

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  31. Lagraaaange

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  32. I

    Proving a linear algebra equation

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  33. C

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  34. c3po

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  35. K

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  36. S

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  37. N

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  38. M

    MHB Matrix Algebra Help: Solve for p1, p2, and p3

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  39. H

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  40. L

    Simple Proofs for Matrix Algebra Properties: A Beginner's Guide

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  41. T

    Programs Differential Equations or Matrix Algebra for Physic Major

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  42. K

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  43. D

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  44. N

    Matrix Alalysis, Matrix Algebra, Linear Algebra, what's the difference?

    Matrix Alalysis, Matrix Algebra, Linear Algebra, they seem to cover many similar topics. Would someone explain about what are the differences between them? Thanks in advance.
  45. H

    Engineering Physics, Diff EQ, Matrix Algebra - too hard?

    Hello, I am currently signed up for Fall Quarter Engineering Physics, Diff EQ, and Matrix algebra at the University of Washington. Right now I am sort of skeptical if I should drop one of these classes because I have heard horror stories from at least one of each of these classes. I got a B-...
  46. V

    How to Calculate T(2, -1, 1) Using Given Linear Transformations?

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  47. S

    Matrix Algebra (Recurrences & Diagonalisation)

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  48. B

    Matrix Algebra Homework: Solving a 6x2 Matrix with Variables to the Second Power

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  49. R

    Help with simple matrix algebra

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  50. P

    Solve X', X for Y: Matrix Algebra Help

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