Linear and Abstract Algebra Forum

Post thread
Join experts in discussing linear and abstract algebra topics. This includes vector spaces and linear transformations. Also groups and other algebraic structures along with Number Theory.
Primes in set of rational numbers
  • · Replies 8 ·
Replies
8
Views
3K
Principle of Induction and Principle of Well-Ordering
  • · Replies 1 ·
Replies
1
Views
4K
Help deriving integer sequence formula
  • · Replies 1 ·
Replies
1
Views
4K
Coefficients in expansion of product(1-x^a, a=1n)?
  • · Replies 5 ·
Replies
5
Views
3K
What Transformation Matrix Defines the Metric Tensor?
  • · Replies 10 ·
Replies
10
Views
13K
HiSo I'm looking at presentations.I think that I understand that
  • · Replies 1 ·
Replies
1
Views
2K
Uniqueness of the roots of a polynomial equation
  • · Replies 8 ·
Replies
8
Views
4K
What is the proof of Euler's function?
  • · Replies 3 ·
Replies
3
Views
4K
Irreducible representation of S3
  • · Replies 3 ·
Replies
3
Views
8K
Recursive series for sum of 2 powers
  • · Replies 1 ·
Replies
1
Views
3K
Questions about the basic properties of Integers
  • · Replies 5 ·
Replies
5
Views
4K
Is There a Topological or Geometrical Approach to the Riemann Hypothesis?
  • · Replies 3 ·
Replies
3
Views
3K
Finding A to the power of n without using eigenvalues
  • · Replies 2 ·
Replies
2
Views
7K
Find the projection of the vector (1,1,0,1)
  • · Replies 1 ·
Replies
1
Views
2K
How to Make Initial Guesses for Parameters in a Nonlinear Model?
  • · Replies 1 ·
Replies
1
Views
2K
Why is phi(n) always an even number?
  • · Replies 3 ·
Replies
3
Views
13K
Understanding Semi-Direct Products in Group Theory and Lie Algebras
  • · Replies 3 ·
Replies
3
Views
2K
Help with proof of theorem related to Fermat's.
  • · Replies 3 ·
Replies
3
Views
3K
Coordinate Transformation & Jacobian Matrix
  • · Replies 3 ·
Replies
3
Views
7K
Localization in integral domains
  • · Replies 3 ·
Replies
3
Views
5K
Category theory - right adjoint problem
  • · Replies 2 ·
Replies
2
Views
2K
Goldbach's Conjecture - Proof (better link)
  • · Replies 48 ·
2
Replies
48
Views
13K
Is Every Root of 2 Higher Than 1 Irrational?
  • · Replies 6 ·
Replies
6
Views
3K
Solving a Question on Abstract Algebra - Help Needed
  • · Replies 2 ·
Replies
2
Views
2K
What Are the Advantages of Base Twelve Over Other Number Bases?
  • · Replies 34 ·
2
Replies
34
Views
12K
What is V-representable and how is it used?
  • · Replies 4 ·
Replies
4
Views
4K
Greatest common divisor | Relatively prime
  • · Replies 45 ·
2
Replies
45
Views
14K
Straight Line from polar co-ordinates
  • · Replies 2 ·
Replies
2
Views
3K
Find the Best Cryptography Books for Beginners - Tips and Recommendations
  • · Replies 4 ·
Replies
4
Views
3K
Why Are Rings in Abstract Algebra Important?
  • · Replies 3 ·
Replies
3
Views
2K
Need general algorithm for finding dual bases
  • · Replies 10 ·
Replies
10
Views
6K
Vector Cross Product: R4 Vectors & Permutation Symbol
  • · Replies 5 ·
Replies
5
Views
19K
Group A is a quotient of Group B ?
  • · Replies 8 ·
Replies
8
Views
3K
How Does a Linear Transformation T with T^2 = T Affect Vectors in V?
  • · Replies 1 ·
Replies
1
Views
4K
How to show SU(n) is a normal subgroup of U(n)
  • · Replies 3 ·
Replies
3
Views
4K
Calculate the abeliazation of the group G=<a,b>
  • · Replies 1 ·
Replies
1
Views
2K
Getting started with symmetry groups
  • · Replies 1 ·
Replies
1
Views
2K
Matrix Multiplication for Vertical Vectors
  • · Replies 10 ·
Replies
10
Views
2K
What happens to the eigenvalues when a constant is multiplied to a matrix?
  • · Replies 1 ·
Replies
1
Views
2K
Does the Greatest Common Divisor of a and b Divide c in the Equation Ax+by=c?
  • · Replies 13 ·
Replies
13
Views
13K
A simple question on representations and tensor products
  • · Replies 6 ·
Replies
6
Views
2K
What Is the Symmetry Group of the Equation \( x^4 + a^2 = 0 \)?
  • · Replies 1 ·
Replies
1
Views
2K
Sum of Digits & Divisibility by 3: Explained
  • · Replies 2 ·
Replies
2
Views
8K
Question on cyclic groups (addition mod n)
  • · Replies 14 ·
Replies
14
Views
5K
Understanding Associativity of Multiplication Modulo n
  • · Replies 1 ·
Replies
1
Views
4K
Proving G cannot Equal HK When K Contains a Conjugate of H
  • · Replies 2 ·
Replies
2
Views
2K
Dissected Number Law: Math Poetry & Formula
  • · Replies 26 ·
Replies
26
Views
9K
Physical applications of matrix congruence?
  • · Replies 8 ·
Replies
8
Views
4K
What Are Fundamental and Unitary Representations in Mathematics?
  • · Replies 4 ·
Replies
4
Views
2K
Further questions on the basics of Lie Algebras
  • · Replies 4 ·
Replies
4
Views
3K
For all solutions of n and m that satisfy.
  • · Replies 3 ·
Replies
3
Views
2K
Understanding P-adic Numbers: A Primer
  • · Replies 5 ·
Replies
5
Views
4K
Singular values of a matrix times a diagonal matrix
  • · Replies 1 ·
Replies
1
Views
6K
PF tensor product space equation
  • · Replies 1 ·
Replies
1
Views
2K
What is the equation for representing a linear operator in terms of a matrix?
  • · Replies 2 ·
Replies
2
Views
10K
How to Solve a Rectangle Perimeter Inequality in Algebra
  • · Replies 1 ·
Replies
1
Views
2K
Can This Mathematical Equation Be Solved for All Prime Numbers?
  • · Replies 2 ·
Replies
2
Views
3K
A question on irreducible representation
  • · Replies 3 ·
Replies
3
Views
3K
Add/Subtract Linear Equations to Solve for Variable
  • · Replies 7 ·
Replies
7
Views
5K
What are the properties of rotation axes in N-dimensions?
  • · Replies 10 ·
Replies
10
Views
6K
How is the Tensor Product of Vector Spaces Constructed?
  • · Replies 12 ·
Replies
12
Views
9K
Is a Superalgebra with Only Three Basis Possible?
  • · Replies 1 ·
Replies
1
Views
2K
Triangular Number Equation: a*T(b) + b^2*T(a-1) = b*T(a) + a^2*T(b-1)
  • · Replies 2 ·
Replies
2
Views
3K
Help Prove Real Eigenvalues of Symmetric Matrix
  • · Replies 4 ·
Replies
4
Views
2K
Perpendicularity on complex vector space
  • · Replies 5 ·
Replies
5
Views
4K
Is There a Name for the Decomposition of a Partitioned Orthogonal Matrix?
  • · Replies 1 ·
Replies
1
Views
4K
Constructing Ring over Monoid: Questions & Answers
  • · Replies 3 ·
Replies
3
Views
3K
Calculating Prime Number Counts Using PI(N) Formula up to 10^23
  • · Replies 5 ·
Replies
5
Views
4K
On the multiplicity of the eigenvalue
  • · Replies 2 ·
Replies
2
Views
2K
Proof dim(U+V)=dim U+dim V - dim(U∩V)
  • · Replies 11 ·
Replies
11
Views
4K
Covariant derivatives in Wolfram Math
  • · Replies 1 ·
Replies
1
Views
5K
Is the Transitivity of Ideals Always Guaranteed in Rings?
  • · Replies 7 ·
Replies
7
Views
2K
Programming libraries for C linear algebra
  • · Replies 3 ·
Replies
3
Views
15K
Unpacking the Objects in the Category of Sets: Cardinality and Distinctions
  • · Replies 4 ·
Replies
4
Views
3K
Can an Equation Solver Handle Lattice Functions with Join and Meet Operators?
  • · Replies 1 ·
Replies
1
Views
4K
Direct Sum vs Direct Product of Rings: Irish & Rosen
  • · Replies 2 ·
Replies
2
Views
3K
Visualizing Subspaces and Subsets (in R3)
  • · Replies 3 ·
Replies
3
Views
6K
Is There a General Formula for Finding the Nth Power of a 2x2 Matrix?
  • · Replies 4 ·
Replies
4
Views
18K
Discussion group for abstract algebra? I'd be interested
  • · Replies 4 ·
Replies
4
Views
3K
Is Godel's incompletness theorem complete?
  • · Replies 12 ·
Replies
12
Views
7K
What is a Vector? Geometric & Algebraic Definitions
  • · Replies 16 ·
Replies
16
Views
4K
Analyzing a Proof of Phi-Function Multiplicativity
  • · Replies 6 ·
Replies
6
Views
4K
Prove Lagrange Polynomials Basis of $\mathbb{R}_{n}[X]
  • · Replies 4 ·
Replies
4
Views
2K
Is a projection operator hermitian?
  • · Replies 3 ·
Replies
3
Views
15K
How do transformations in group G relate to curves in Lie algebras?
  • · Replies 5 ·
Replies
5
Views
3K
Number Theory proof linked to decimals
  • · Replies 5 ·
Replies
5
Views
4K
How Can We Prove the Extension of Bezout's Identity?
  • · Replies 13 ·
Replies
13
Views
7K
How Does the Euclidean Algorithm Scale with Multiplication Factors?
  • · Replies 1 ·
Replies
1
Views
6K
Eigenvalue Theorem: Proof of Det(A - λI_n)=0
  • · Replies 5 ·
Replies
5
Views
8K
Delta function for grassmann numbers?
  • · Replies 4 ·
Replies
4
Views
7K
Finding Jordan forms over the complex numbers
  • · Replies 2 ·
Replies
2
Views
2K
Question about spherical harmonics
  • · Replies 1 ·
Replies
1
Views
2K
What Impact Do Large Mersenne Primes Have on Mathematical Research?
  • · Replies 3 ·
Replies
3
Views
2K
Retrieving angle of rotation from transformation matrix
  • · Replies 2 ·
Replies
2
Views
8K
Is {v1,...,vk} Linearly Independent Given vi.vj=0 When i≠j?
  • · Replies 2 ·
Replies
2
Views
3K
Coordinate Transformations Question
  • · Replies 2 ·
Replies
2
Views
2K
Difference between dimension and rank
  • · Replies 4 ·
Replies
4
Views
29K
Solve Linear Algebra Exam: Find a Basis of U & Orthogonal Complement
  • · Replies 2 ·
Replies
2
Views
4K
The worst case for trial division factorisation of n?
  • · Replies 9 ·
Replies
9
Views
4K
Eigenvalue of 3D rotation matrix
  • · Replies 2 ·
Replies
2
Views
8K