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Abstract Algebra
Have you ever wondered what would happen if you redefined some of the basic rules of algebra so that concepts you took for granted, like AB = BA, no longer apply? Abstract algebra does just that through the study of the properties that define algebraic structures. Post all questions about fields, rings, group theory, vector spaces, and the axioms that define them into this category.
1,849 Questions
What is the numbers of groups of order 8 upto isomorphisms?
There are five groups of order 8: three of them are Abelian and the other two are not.
These are
1. C8, the group generated by a where a8 = 1
2. C4xC2, the group generated by a and b where a4 = b2 = 1
3. C2xC2xC2, the group generated by a, b and c where a2 = b2 = c2= 1
4. the dihedral group
5. the quaternion group
What is the difference between zero matrix and null matrix?
there is none you weasel. the only good matrix is revolutions. :)
What is the value of a model s7102083?
It looks like you have listed a serial number, not a model number. You need to provide a detailed description that tells who made it, what type of finish it has, the barrel length, the caliber/gauge, engraving (if any) and all markings.
24X - 3 is an expression whose value depends on X. Since that is not known, it is not possible to answer the question.
First, a small note: an m-by-n or m x n matrix has m rows and n columns.
- The eigenvalues λ of a matrix A are scalars such that Ax = λx for some nonzero x vector.
- The entries aij of a matrix A are the numbers contained within the matrix, each with a unique position of the ith row and jth column.
- 'Equality' in matrices has the same definition as for the rest of mathematics.
- A matrix of groups is a matrix whose entries are members of a group, often with specific entries in certain positions.
- The matrix identity In is that square n by n matrix whose entries aij are 1 if i = j, and 0 if i ≠j.
- The inverse of a square matrix A is the square matrix B such that AB = In, denoted by B = A-1.
- Matrix multiplication is the act of combining two matrices, the p-by-q A = (aij) and the q-by-r B = (bij) to form the new matrix p-by-r C = (cij) such that cij = Σaikbkj, where 1 ≤ k ≤ q. This is denoted by C = AB. Note that matrix mulplication is not commutative, i.e. AB does not necessarily equal BA; the order of the components is important and must be maintained to achieve the result. Note also that although p does not need to equal r, q must be the same in each matrix.
Why a linear transformer is called linear?
That is because they are of the form
y = a1x1 + a2x2 + ... anxn where x1, ... xn are variables and a1, ..., an are constants.
Such an equation represents a straight line in n-dimensional space.
When a system has two variables each solution is an ordered pair true or false?
True. That's a way of representing the solution.
Write a C program using dynamic memory allocation to find the sum of elements of a matrix?
Did you know that memory allocation is not needed to display the matrix? However, the C program is to find the sum of all the elements.
How do you prove ax5 plus bx4 plus cx3 plus dx2 plus ex plus f equals 0 is not solvable?
This is called the Abel-Ruffini theorem.
Is it true that an infinite cyclic group may have 3 distinct generators?
An example of an infinite cyclic group is the integers with addition. This group is generated by 1.
