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.
Explaining the Riemann Hypothesis and Other Famous Math Problems
  • · Replies 4 ·
Replies
4
Views
7K
Basis of Vector Space V: Subset of B = Basis of U?
  • · Replies 11 ·
Replies
11
Views
3K
Quick Question About Tensor Products
  • · Replies 9 ·
Replies
9
Views
3K
Where Can I Find Online Lectures for Linear Algebra?
  • · Replies 5 ·
Replies
5
Views
23K
Fermat Last Theorem: a^n+b^n<c^n
  • · Replies 22 ·
Replies
22
Views
3K
Prime Number Formulas: Find the Nth Prime
  • · Replies 48 ·
2
Replies
48
Views
14K
How to Compute Eigenvectors for Large Matrices Efficiently?
  • · Replies 9 ·
Replies
9
Views
13K
Is the Set of Products of Two Ideals Always an Ideal?
  • · Replies 2 ·
Replies
2
Views
3K
Constructing Proofs in Mathematics: Where do I Begin?
  • · Replies 5 ·
Replies
5
Views
3K
Constructing the Generators of SU(8) Group in String Theory
  • · Replies 3 ·
Replies
3
Views
3K
How Do We Prove \(\forall n\in\mathbb{N}\;\varphi(n)\mid n\) Is False?
  • · Replies 10 ·
Replies
10
Views
3K
For lack of a better word, Modifiers.
  • · Replies 16 ·
Replies
16
Views
5K
Linearly independent but not orthogonal, how come?
  • · Replies 4 ·
Replies
4
Views
49K
Eigenvalues of A: Same Eigenspaces for A^-1, Transpose, A^k
  • · Replies 8 ·
Replies
8
Views
3K
Can Infinite Sets Still Form Groups Under Closure Conditions?
  • · Replies 29 ·
Replies
29
Views
7K
Question regarding multiple steps in linear mapping
  • · Replies 1 ·
Replies
1
Views
2K
Simple prime/GCD proof question
  • · Replies 2 ·
Replies
2
Views
5K
How Do You Rotate One Vector to Another and Apply the Same Rotation to a Matrix?
  • · Replies 1 ·
Replies
1
Views
6K
Pascal Triangle & Its Applications.
  • · Replies 7 ·
Replies
7
Views
12K
Understanding Summation and Latex: A Simple Explanation
  • · Replies 3 ·
Replies
3
Views
4K
  • Poll Poll
Barry Mazur's current BAMS article
  • · Replies 2 ·
Replies
2
Views
3K
How to diagonalize NxNxNxN matrix
  • · Replies 4 ·
Replies
4
Views
10K
Solve Cryptography Exercises: Rabbin & RSA Protocols
  • · Replies 5 ·
Replies
5
Views
3K
Solving Radicals for A,B,C and D: 2^11-1
  • · Replies 5 ·
Replies
5
Views
3K
Why not randomness for primes' distribution?
  • · Replies 20 ·
Replies
20
Views
6K
Can a Finitely Generated Group Contain an Infinitely Generated Subgroup?
  • · Replies 2 ·
Replies
2
Views
2K
Connection between polynomials and groups
  • · Replies 3 ·
Replies
3
Views
2K
Dimension of eigenspace, multiplicity of zero of char.pol.
  • · Replies 5 ·
Replies
5
Views
11K
Having difficulty with an Ax=b problem and understanding it
  • · Replies 10 ·
Replies
10
Views
4K
Proving a Subgroup of a Solvable Group is Solvable
  • · Replies 5 ·
Replies
5
Views
4K
Prime factorization of rationals
  • · Replies 4 ·
Replies
4
Views
6K
Euler's theorem as primality test?
  • · Replies 6 ·
Replies
6
Views
5K
Is it possible to multiply by 'undefined'?
  • · Replies 7 ·
Replies
7
Views
18K
Riemann Hypothesis: Question on Critical Line
  • · Replies 2 ·
Replies
2
Views
3K
Is Tensor Product Uniqueness Dependent on the Choice of Linear Functions?
  • · Replies 9 ·
Replies
9
Views
3K
What Can We Learn from Finite Presentations of Groups?
  • · Replies 7 ·
Replies
7
Views
3K
What Does It Mean for a Group to Be Generated by Two Subgroups?
  • · Replies 19 ·
Replies
19
Views
11K
Transforms that Preserve The Dominant Eigenvector?
  • · Replies 1 ·
Replies
1
Views
2K
Field on R^3 and isomorphism between C and R
  • · Replies 5 ·
Replies
5
Views
4K
Ancient Numbers: Expressing Values, Devision & Subtraction
  • · Replies 9 ·
Replies
9
Views
6K
Eigenvalue kind of nilpotent problem
  • · Replies 2 ·
Replies
2
Views
2K
Understanding Oiler's Approach to the Zetha Function: A Math Book Review
  • · Replies 8 ·
Replies
8
Views
4K
Find the point D such that all the triangles have the same area.
  • · Replies 1 ·
Replies
1
Views
2K
What is the significance of the structure of numbers?
  • · Replies 12 ·
Replies
12
Views
4K
Proving Let A & B be Square Matrices of n x n & AB = 0n
  • · Replies 4 ·
Replies
4
Views
2K
Proving the Unsolvable: Lagrange's Theorem and 4 Squares
  • · Replies 4 ·
Replies
4
Views
4K
Boolean Algebra: What Audio Engineering Majors at UMiami Need to Know
  • · Replies 1 ·
Replies
1
Views
2K
Units and prime elements in euclidean rings
  • · Replies 10 ·
Replies
10
Views
7K
Adjoint Multiplicity: A* x A* = (A^2)*?
  • · Replies 11 ·
Replies
11
Views
3K
Normed space and its double dual
  • · Replies 1 ·
Replies
1
Views
3K
Why is the trivial ring excluded in the definition of a field?
  • · Replies 4 ·
Replies
4
Views
3K
Recognizing a product of two 3d rotations (matrices)
  • · Replies 4 ·
Replies
4
Views
3K
Exploring Bertrand's Postulate: Maximal Prime Gaps and Conjectures
  • · Replies 7 ·
Replies
7
Views
5K
Symbolic Vector Manipulation Software?
  • · Replies 6 ·
Replies
6
Views
4K
How Can a Cyclic Group Define a Field Using Only Addition?
  • · Replies 8 ·
Replies
8
Views
3K
Learn Linear Algebra Before Calculus?
  • · Replies 9 ·
Replies
9
Views
52K
What is the formula for finding the determinant of a 10x10 matrix?
  • · Replies 13 ·
Replies
13
Views
19K
Is My Integer Factorization Algorithm Flawed?
  • · Replies 9 ·
Replies
9
Views
7K
What Is the Tensor Product of Vector Spaces?
  • · Replies 33 ·
2
Replies
33
Views
14K
Casey's thread of annoying Linear Algebra questions
  • · Replies 7 ·
Replies
7
Views
3K
Verifying a Finite Non-Abelian Group with Set of 2x2 Matrices Modulo p
  • · Replies 7 ·
Replies
7
Views
6K
Linear programming bank assets problem
  • · Replies 3 ·
Replies
3
Views
7K
Iteration of Euler's phi function
  • · Replies 1 ·
Replies
1
Views
6K
Formally Proving the Invariance of Solutions in Gaussian Elimination
  • · Replies 1 ·
Replies
1
Views
4K
Using an accelerometer to measure speed
  • · Replies 3 ·
Replies
3
Views
15K
What Structure Must G Have for All Aut(G) Elements to Send N to N
  • · Replies 5 ·
Replies
5
Views
3K
Sum of Reciprocals of Prime Numbers Equals 1
  • · Replies 3 ·
Replies
3
Views
3K
Sum of Primes < n Formula - Pseudot's Research
  • · Replies 1 ·
Replies
1
Views
9K
Finding the face of an icosahedron in which a vector falls in
  • · Replies 4 ·
Replies
4
Views
3K
Predicting the Period of Recurring Decimals in Rational Numbers
  • · Replies 5 ·
Replies
5
Views
4K
Solvable polynomial definition problem
  • · Replies 5 ·
Replies
5
Views
3K
What to do with a zero column in a system of linear equations?
  • · Replies 4 ·
Replies
4
Views
9K
The (i,j)-minor of a matrix: multilinear map?
  • · Replies 2 ·
Replies
2
Views
3K
Lang's Algebra Ch 1 Problem 12(c): Ambiguous Group Law
  • · Replies 2 ·
Replies
2
Views
3K
Way to generalize the relationship between T and T^2?
  • · Replies 9 ·
Replies
9
Views
4K
Cardinality of a basis of an infinite-dimensional vector space
  • · Replies 7 ·
Replies
7
Views
11K
What Are Some Examples of Isomorphic Vector Spaces with Different Dimensions?
  • · Replies 5 ·
Replies
5
Views
7K
Conjugacy in Algebra: Why Does a=g^-1bg Occur?
  • · Replies 2 ·
Replies
2
Views
2K
Is u + v in U if u and v are elements of V but not in U?
  • · Replies 1 ·
Replies
1
Views
2K
How Do We Calculate (f O g) for Given Functions and Set A?
  • · Replies 4 ·
Replies
4
Views
3K
Understanding Stirling's Formula: The Bent Equals Sign Explained
  • · Replies 11 ·
Replies
11
Views
3K
How many ways we can represent 50 as the sum of two primes?
  • · Replies 1 ·
Replies
1
Views
3K
Generalized eigenspace invariant?
  • · Replies 2 ·
Replies
2
Views
4K
The module is injective iff it is a direct summand of an injective cogenerator
  • · Replies 1 ·
Replies
1
Views
3K
Proving Cauchy-Schwarz Inequality: My Dumb Question
  • · Replies 4 ·
Replies
4
Views
3K
Proving R^n Can Be a Field: The n>2 Case
  • · Replies 3 ·
Replies
3
Views
2K
Vector Spaces: Real Numbers Over Rational Numbers
  • · Replies 2 ·
Replies
2
Views
2K
How many whole numbers c make x^2 + c a multiple of 2^2007?
  • · Replies 6 ·
Replies
6
Views
3K
Geometric Algebra: Signs of electromagnetic field tensor components?
  • · Replies 10 ·
Replies
10
Views
7K
Simple counterexample for claim about integral domains
  • · Replies 6 ·
Replies
6
Views
4K
Program for graphing Riemann zeta function
  • · Replies 4 ·
Replies
4
Views
7K
Minimum Number of Distinct Values for a Polynomial over a Finite Field
  • · Replies 8 ·
Replies
8
Views
4K
How to Study for an Algebra Test on Vectors and Matrices?
  • · Replies 3 ·
Replies
3
Views
3K
Finding Constants for Linear Dependence in 3D Vectors
  • · Replies 4 ·
Replies
4
Views
4K
Understand the Difference Between Trivial and Non-Trivial Solutions
  • · Replies 2 ·
Replies
2
Views
12K
What Are Cyclic Quadratic Residues and Their Sums Modulo Prime Numbers?
  • · Replies 2 ·
Replies
2
Views
4K
Positive Operator: Why Is \sqrt{A^*A} Positive?
  • · Replies 3 ·
Replies
3
Views
5K
Proving a Property of Quadratic Nonresidues in Prime Numbers
  • · Replies 15 ·
Replies
15
Views
6K
How can I calibrate an accelerometer with unequal sensitivity between axes?
  • · Replies 5 ·
Replies
5
Views
15K
What Are Canonical Coordinates and How to Convert a Basis in R^2?
  • · Replies 2 ·
Replies
2
Views
3K