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.
Proving a set of derivatives to be a subset of real functions
  • · Replies 4 ·
Replies
4
Views
3K
Shortcut method for order 4 and above.
  • · Replies 4 ·
Replies
4
Views
7K
An efficient way to find perfect squares?
  • · Replies 15 ·
Replies
15
Views
9K
Proving a set to be a vector space,
  • · Replies 5 ·
Replies
5
Views
4K
Determining the Number of Invertible Elements in Zn
  • · Replies 13 ·
Replies
13
Views
13K
Is Every Complex Matrix Similar to Its Transpose?
  • · Replies 2 ·
Replies
2
Views
8K
Galois Theory Intro Cut Short - Seeking Resources
  • · Replies 2 ·
Replies
2
Views
4K
True or false eigenvalue problem
  • · Replies 2 ·
Replies
2
Views
3K
Bilinear Forms associated With a Quadratic Form over Z/2
  • · Replies 3 ·
Replies
3
Views
4K
Solution to System with Unknown Variables n > 4
  • · Replies 4 ·
Replies
4
Views
2K
How can I find a basis for the span of some eigenvectors?
  • · Replies 2 ·
Replies
2
Views
4K
Counting continued fraction numbers
  • · Replies 3 ·
Replies
3
Views
4K
Grothendieck decompostion simple example
  • · Replies 1 ·
Replies
1
Views
3K
External direct product- homomorphism
  • · Replies 7 ·
Replies
7
Views
4K
Additive Prime Numbers: Is There Anything Known About them?
  • · Replies 2 ·
Replies
2
Views
7K
Can't get my head into vector spaces and subspaces
  • · Replies 6 ·
Replies
6
Views
5K
Nonzero R-Module over commuttaive ring, all submodules free => R PID?
  • · Replies 6 ·
Replies
6
Views
4K
Why Is Proving the Infinity of Fibonacci Primes So Challenging?
  • · Replies 6 ·
Replies
6
Views
6K
Rings as Algebras: Definitions & Questions
  • · Replies 7 ·
Replies
7
Views
3K
Wiles Proof of Fermat's Last Theorem
  • · Replies 1 ·
Replies
1
Views
3K
Understanding Graham's Number: A Comprehensive Guide
  • · Replies 5 ·
Replies
5
Views
10K
Ellipsoid algebra: converting forms
  • · Replies 1 ·
Replies
1
Views
4K
Can Least Squares be Applied to Matrices for Solving a Complex Equation?
  • · Replies 8 ·
Replies
8
Views
4K
Notation in linear algebra and rule for square of matrix norm
  • · Replies 2 ·
Replies
2
Views
4K
Number Theory, Linear & Abstract Algebra
  • · Replies 13 ·
Replies
13
Views
5K
Finite-Index Subgroups of Infinite Groups.
  • · Replies 8 ·
Replies
8
Views
6K
Confused about the concepts of dual spaces, dual bases, reflexivity and annihilators
  • · Replies 32 ·
2
Replies
32
Views
21K
Question on maximal ideals in an integral domain
  • · Replies 2 ·
Replies
2
Views
2K
Why cant i learn linear algebra?
  • · Replies 11 ·
Replies
11
Views
8K
Why do vector multiplications result in different types of quantities?
  • · Replies 7 ·
Replies
7
Views
5K
Difficult linear algebra problem
  • · Replies 1 ·
Replies
1
Views
4K
Composition of permutation cycles
  • · Replies 1 ·
Replies
1
Views
3K
|a+b| = |a| + |b| implies a and b parallel?
  • · Replies 3 ·
Replies
3
Views
3K
How can a column vector be transformed into a diagonal matrix?
  • · Replies 3 ·
Replies
3
Views
4K
Finding rotation matrix with given new and old frame
  • · Replies 3 ·
Replies
3
Views
7K
Understanding Tensors: Comparing gαβAβ and Aβgαβ
  • · Replies 10 ·
Replies
10
Views
3K
Examining the Taylor Series - Confused?
  • · Replies 2 ·
Replies
2
Views
2K
Dirichlet's Theorem on Arithmetic Progressions
  • · Replies 2 ·
Replies
2
Views
4K
Why is the number of fixed points divisible by p in Cauchy's Theorem proof?
  • · Replies 4 ·
Replies
4
Views
5K
If x and y are parallel, then ha = b?
  • · Replies 1 ·
Replies
1
Views
2K
Modern Algebra & Real Analysis: Learn Proofwriting?
  • · Replies 9 ·
Replies
9
Views
5K
Finding Area Under a Helix: A Stumper Problem
  • · Replies 8 ·
Replies
8
Views
12K
The proof that an odd perfect number does not exist
  • · Replies 6 ·
Replies
6
Views
11K
Matrix multiplication preserve order Block matrix
  • · Replies 2 ·
Replies
2
Views
3K
Existence of Roots for Quadratic Forms Modulo Prime Numbers
  • · Replies 9 ·
Replies
9
Views
5K
Orthogonal Basis in 3d is flipping.
  • · Replies 14 ·
Replies
14
Views
4K
What is the Connection Between Rank and Free Modules?
  • · Replies 6 ·
Replies
6
Views
5K
Proving LCM Formula and GCD for Non-Integers
  • · Replies 59 ·
2
Replies
59
Views
14K
Column Space of A'*A: Subset of A'?
  • · Replies 1 ·
Replies
1
Views
3K
Matrix form - completing the square
  • · Replies 1 ·
Replies
1
Views
6K
How Can Analogies Simplify Group, Ring, and Field Concepts?
  • · Replies 1 ·
Replies
1
Views
3K
Dot/bilinear product in C^n / Orthogonality
  • · Replies 1 ·
Replies
1
Views
2K
Understanding Transvections:T_W:V->V Tv=v+w
  • · Replies 3 ·
Replies
3
Views
3K
When Does a Square Matrix Ensure Unique Solutions?
  • · Replies 2 ·
Replies
2
Views
8K
Can C= (pi)d Be Solved with Any Prime Values?
  • · Replies 2 ·
Replies
2
Views
4K
Confused about definition of algebraic closure
  • · Replies 3 ·
Replies
3
Views
4K
Is this correct? Field extension of the rationals
  • · Replies 10 ·
Replies
10
Views
4K
What was the motivation to define what a vector space is?
  • · Replies 3 ·
Replies
3
Views
5K
Eigenvalues of a symmetric operator
  • · Replies 9 ·
Replies
9
Views
5K
Same symbol, different meanings? Subgroup index & field extension
  • · Replies 3 ·
Replies
3
Views
3K
Counting Cycles in S_5: Examining Conjugacy Classes and Lengths
  • · Replies 1 ·
Replies
1
Views
3K
Testing optimality via complementary slackness
  • · Replies 2 ·
Replies
2
Views
3K
Brocard's Problem: No Solution for n! Containing Prime^2, n>7?
  • · Replies 3 ·
Replies
3
Views
5K
  • Poll Poll
Find the sum in this given question very interesting and analytical
  • · Replies 18 ·
Replies
18
Views
5K
Finitely generated modules as free modules
  • · Replies 10 ·
Replies
10
Views
7K
Transforming association matrix to a functional matrix
  • · Replies 1 ·
Replies
1
Views
2K
How to Prove Aut(H ⊕ K) ≅ Aut(H) ⊕ Aut(K)?
  • · Replies 5 ·
Replies
5
Views
2K
Understanding Square Residue: Solving the Mystery of -1 = x^2 mod p
  • · Replies 4 ·
Replies
4
Views
4K
Is W a Subspace of R^3 and What is Its Geometry?
  • · Replies 1 ·
Replies
1
Views
3K
Determining whether sets of matrices in a vectorspace are linearly independent?
  • · Replies 2 ·
Replies
2
Views
4K
Webpage title: How to Solve a 3D Matrix Equation
  • · Replies 6 ·
Replies
6
Views
6K
Word for one-to-one correspondence between ideals and modules of an algebra
  • · Replies 2 ·
Replies
2
Views
3K
Why Is the Transpose of a Matrix Important in Linear Algebra?
  • · Replies 2 ·
Replies
2
Views
3K
Group representations on tensor basis.
  • · Replies 5 ·
Replies
5
Views
3K
Theorem of mutations in a numeral sequence
  • · Replies 2 ·
Replies
2
Views
4K
Request for introductory book on graph theory
  • · Replies 3 ·
Replies
3
Views
3K
Need help starting a proof about an infinite square grid.
  • · Replies 1 ·
Replies
1
Views
4K
[Linear Algebra]- Simultaneous equation. Deriving the general solution.
  • · Replies 10 ·
Replies
10
Views
4K
Find subgroups of finitely generated abelian groups
  • · Replies 1 ·
Replies
1
Views
3K
Does the Picard Group Vanish for Semilocal Rings?
  • · Replies 2 ·
Replies
2
Views
3K
Two Prime Fields Isomorphic to Zp and Zq
  • · Replies 1 ·
Replies
1
Views
2K
Why Does H ∩ K = {e} Imply G Has Only One Element of Order 3?
  • · Replies 12 ·
Replies
12
Views
3K
Convex set for similarity constraint
  • · Replies 2 ·
Replies
2
Views
2K
Formulation of a linear programming model
  • · Replies 1 ·
Replies
1
Views
3K
Calculating angles between matrices
  • · Replies 4 ·
Replies
4
Views
20K
Sum of squares of prime factors
  • · Replies 8 ·
Replies
8
Views
7K
Derived Subgroup (In particular Q8)
  • · Replies 1 ·
Replies
1
Views
5K
Formula for multiplication of trinomials
  • · Replies 2 ·
Replies
2
Views
3K
Linear Transformation to Block-wise Stack Matrix
  • · Replies 11 ·
Replies
11
Views
4K
Simple Hyperplane Equation - What am I Missing?
  • · Replies 3 ·
Replies
3
Views
2K
How can the Cauchy-Schwarz inequality be applied to L^2 functions in a book?
  • · Replies 8 ·
Replies
8
Views
4K
Does the Chain Rule Apply to Derivatives of Inner Products?
  • · Replies 1 ·
Replies
1
Views
12K
Convolution and a specific function
  • · Replies 2 ·
Replies
2
Views
2K
Solve Linear Algebra Matrix Equation
  • · Replies 8 ·
Replies
8
Views
3K
Paradox for the existence of 4,5 and 7 using Brocard's problem
  • · Replies 3 ·
Replies
3
Views
4K
Rank of Matrix A with Kronecker Symbol and Sum Condition
  • · Replies 3 ·
Replies
3
Views
3K
Proof of FLT Using High School Algebra & Number Theory
  • · Replies 20 ·
Replies
20
Views
8K
What is the Visual Prime Pattern Based on Trig and Harmonics?
  • · Replies 112 ·
4
Replies
112
Views
35K
Where Did the Binomial Theorem Originate?
  • · Replies 6 ·
Replies
6
Views
4K
Complex Numbers in Linear Algebra
  • · Replies 3 ·
Replies
3
Views
3K