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.
What is the Difference Between Factor Space and Equivalence Classes?
  • · Replies 1 ·
Replies
1
Views
2K
Orthogonality & Dual Spaces: Exploring Physical Quantities in Vector Spaces
  • · Replies 9 ·
Replies
9
Views
3K
How to prove that a set is a group? related difficult/challenge quesyion.
  • · Replies 6 ·
Replies
6
Views
9K
Playing with Small Natural Numbers Network
  • · Replies 3 ·
Replies
3
Views
3K
Derivative of a function with matrices
  • · Replies 10 ·
Replies
10
Views
3K
Proving Congruence Classes in Q[√-3] with Prime Divisor λ
  • · Replies 9 ·
Replies
9
Views
4K
Is there a probabilistic approach to number theory conjectures?
  • · Replies 8 ·
Replies
8
Views
3K
Adding 3.6, 4.4, and 5.8: Keeping the Sum 13.8
  • · Replies 1 ·
Replies
1
Views
2K
Tensor Analysis and Linear Algebra, what's the difference
  • · Replies 2 ·
Replies
2
Views
5K
Existence of polynomial in R^2
  • · Replies 1 ·
Replies
1
Views
2K
I've never felt dumber: me understand Fibonacci identity.
  • · Replies 2 ·
Replies
2
Views
2K
Why C([0,1]) and C_{o} are not isomorphic?
  • · Replies 12 ·
Replies
12
Views
3K
Understanding Associates and Norms in Algebraic Integers
  • · Replies 20 ·
Replies
20
Views
5K
Show one ring not isomorphic to the other
  • · Replies 1 ·
Replies
1
Views
5K
All Eigenvalues Lie on the Unit Circle
  • · Replies 5 ·
Replies
5
Views
7K
Finding the General Term for Perfect Squares
  • · Replies 2 ·
Replies
2
Views
2K
Find and Test Primes using the Chinese Remainder Theorem and Binary Search
  • · Replies 2 ·
Replies
2
Views
6K
Interior Product: Definition, Inner Product & Isomorphism
  • · Replies 3 ·
Replies
3
Views
4K
Proof of Goldbach,Polignac,Legendre,Sophie Germain conjecture.pdf
  • · Replies 2 ·
Replies
2
Views
5K
Why is 3AB+P Set to Zero in Cardan's Cubic Equation?
  • · Replies 3 ·
Replies
3
Views
4K
How Do These Linear Algebra Concepts Align with Definitions and Vector Spaces?
  • · Replies 4 ·
Replies
4
Views
4K
How does this number system conversion algorithm work?
  • · Replies 5 ·
Replies
5
Views
4K
Irreducible Representations and Class
  • · Replies 1 ·
Replies
1
Views
2K
What is the Best Way to Solve This Algebraic Brain Teaser?
  • · Replies 3 ·
Replies
3
Views
3K
Perron formula for matrix powers
  • · Replies 2 ·
Replies
2
Views
3K
Nearest block diagonal matrix to a given matrix
  • · Replies 1 ·
Replies
1
Views
4K
A More Abstract Definition of an Inner Product Space?
  • · Replies 17 ·
Replies
17
Views
6K
Prove Minkowski Inequality using Cauchy-Schwartz Inequality
  • · Replies 3 ·
Replies
3
Views
8K
Eigen-vectors/values under row flipping
  • · Replies 6 ·
Replies
6
Views
3K
Is it possible to simplify the RH problem?
  • · Replies 15 ·
Replies
15
Views
3K
Eisenstein's Irreducibility Criterion
  • · Replies 10 ·
Replies
10
Views
5K
How Do You Prove This Linear Transformation?
  • · Replies 1 ·
Replies
1
Views
2K
How to Find Subgroups of Index 2?
  • · Replies 1 ·
Replies
1
Views
2K
Infinitely many primes in Q[Sqrt(d)]
  • · Replies 9 ·
Replies
9
Views
6K
Pythagorean Theorem: Relationships in Euclidean Space
  • · Replies 9 ·
Replies
9
Views
4K
Linear Combination: Can 1 0 1 0 be Combined?
  • · Replies 2 ·
Replies
2
Views
2K
How do you multiply permutations?
  • · Replies 10 ·
Replies
10
Views
7K
Is There a Simpler Way to Construct a Linear Functional Given a Linear Operator?
  • · Replies 3 ·
Replies
3
Views
3K
A very challenging question regarding in basic algebra group theory?
  • · Replies 2 ·
Replies
2
Views
2K
Invertability as a substitute for looking for linear independence
  • · Replies 3 ·
Replies
3
Views
2K
Linearly Dependent Sets: Answers to Your Questions
  • · Replies 3 ·
Replies
3
Views
2K
Normed division algebras: geometrical limitation
  • · Replies 2 ·
Replies
2
Views
3K
Maximizing Determinant in 3x3 Matrix with 0/1 Entries
  • · Replies 3 ·
Replies
3
Views
10K
How to OLS several lines at once?
  • · Replies 2 ·
Replies
2
Views
2K
Understanding the Proof of Solution Sets in Linear Systems
  • · Replies 4 ·
Replies
4
Views
2K
Solving Complex Number Roots for e^(pi*z)^2 = i | Help Needed
  • · Replies 2 ·
Replies
2
Views
2K
Software that outputs a general polynomial formula for a finite series
  • · Replies 6 ·
Replies
6
Views
5K
Group of order pq && nonnormal subgroup
  • · Replies 3 ·
Replies
3
Views
5K
Are G & H Isomorphic? Prove Answer | Group of 2x2 Matrices
  • · Replies 4 ·
Replies
4
Views
4K
Twin Prime Sieve: Calculate All Twins Less Than N - Todd's Version
  • · Replies 2 ·
Replies
2
Views
4K
Glossary for Linear Algebra + Quick Tips
  • · Replies 4 ·
Replies
4
Views
20K
Permutations of basis elements in Clifford Algebras
  • · Replies 4 ·
Replies
4
Views
3K
Finding Prime Numbers in 2010: Is It Possible?
  • · Replies 11 ·
Replies
11
Views
3K
"Does Finite Group Contain Subgroup of Index 2 if Element has Order 2?
  • · Replies 3 ·
Replies
3
Views
2K
Quaternions and associated manifolds
  • · Replies 10 ·
Replies
10
Views
3K
Linearizing Equations: Finding Square Root of x from Plotted Data
  • · Replies 1 ·
Replies
1
Views
6K
Meaning of colon in group theory, if not subgroup index?
  • · Replies 2 ·
Replies
2
Views
5K
Is there a way to differentiate between numbers
  • · Replies 6 ·
Replies
6
Views
3K
Power System Analysis: Node Elimination Explained
  • · Replies 2 ·
Replies
2
Views
3K
What is the operator between A A^ in A vec = A A^
  • · Replies 5 ·
Replies
5
Views
2K
Understanding the Dimension of a Variety in Algebraic Geometry
  • · Replies 5 ·
Replies
5
Views
3K
Which Interpolation Method for Complex Numbers Is Most Accurate?
  • · Replies 2 ·
Replies
2
Views
7K
Sum of 2 normal numbers still normal?
  • · Replies 8 ·
Replies
8
Views
3K
Relationship of an invertible matrix in spanning set and linear independence
  • · Replies 1 ·
Replies
1
Views
7K
Dimension of SL(2,H), SL(2,R), SL(2,C), SL(2,O) - Proving 15 & 45
  • · Replies 2 ·
Replies
2
Views
4K
Linear Independence: Polynomial Example
  • · Replies 3 ·
Replies
3
Views
12K
How to Calculate Norms of Field Extensions in Galois Theory
  • · Replies 1 ·
Replies
1
Views
2K
Finding eigenvalues and eigenspaces with only this info
  • · Replies 7 ·
Replies
7
Views
3K
What Is the Structure of Left Ideals in Simple Rings?
  • · Replies 3 ·
Replies
3
Views
3K
Understanding the Direct Product of Groups: Applying Group Theory Axioms
  • · Replies 6 ·
Replies
6
Views
4K
How Do Community Members Feel About Our Research?
  • · Replies 3 ·
Replies
3
Views
2K
A thread for learning RSA algorithm
  • · Replies 11 ·
Replies
11
Views
6K
How Can You Verify the Definitions of Homomorphism and Subgroup?
  • · Replies 1 ·
Replies
1
Views
2K
The Power of Group Theory to Success
  • · Replies 1 ·
Replies
1
Views
2K
Arithmetic progression of prime numbers
  • · Replies 2 ·
Replies
2
Views
3K
How Do Unit Quaternions Relate to Spheres and Even-Grade Subalgebras?
  • · Replies 12 ·
Replies
12
Views
5K
Applying the Triple Product in n-dimension
  • · Replies 2 ·
Replies
2
Views
2K
Is W a Subspace of V^3 Given These Vectors?
  • · Replies 4 ·
Replies
4
Views
2K
Can Each Vector Be Made Orthonormal Directly in Gram-Schmidt Process?
  • · Replies 2 ·
Replies
2
Views
2K
What is the connection between row reduction and matrix inversion?
  • · Replies 2 ·
Replies
2
Views
2K
Proof of the Inner Automorphism Theorem for Endomorphism Algebras
  • · Replies 2 ·
Replies
2
Views
2K
How many prime numbers have we actually solved
  • · Replies 8 ·
Replies
8
Views
3K
Semi-Positive Definiteness of Product of Symmetric Matrices
  • · Replies 3 ·
Replies
3
Views
10K
Isomorphism between Order Ideals and Distributive Lattices
  • · Replies 4 ·
Replies
4
Views
3K
Linear Mappings: Examining Bijectivity
  • · Replies 8 ·
Replies
8
Views
2K
Symmetry Groups in Euclidean and Hyperbolic Spaces: A Comparison
  • · Replies 14 ·
Replies
14
Views
5K
Proof of I = R if I Contains a Unit in Commutative Ring
  • · Replies 21 ·
Replies
21
Views
7K
Rational numbers and periodic decimal expansions
  • · Replies 1 ·
Replies
1
Views
4K
What Programming Language Can Handle 30-Digit Integers and Matrices for Free?
  • · Replies 8 ·
Replies
8
Views
4K
Can a Group of Prime Order Be Proven Cyclic Using Only Basic Group Theory?
  • · Replies 1 ·
Replies
1
Views
5K
How do I estimate complex eigenvalues?
  • · Replies 4 ·
Replies
4
Views
11K
How can the prime number theorem be used to understand this proof?
  • · Replies 1 ·
Replies
1
Views
2K
Curious for some insight: inverse of a random matrix is really ordered
  • · Replies 6 ·
Replies
6
Views
4K
Does AB Equal G When |A| + |B| Exceeds |G|?
  • · Replies 5 ·
Replies
5
Views
2K
Beating an old horse .(9) question
  • · Replies 29 ·
Replies
29
Views
8K
Is finding the intersection of two lines in R4 using the same method as in R3?
  • · Replies 2 ·
Replies
2
Views
6K
K-th Prime Proofs & Co-Prime Numbers
  • · Replies 4 ·
Replies
4
Views
4K
Efficient LSV Approximation for Large Matrices | Conjugate Gradient Method Guide
  • · Replies 2 ·
Replies
2
Views
2K
How can I solve simultaneous trigonometric equations involving cosine and sine?
  • · Replies 2 ·
Replies
2
Views
2K
If a mxn matrix A, m>=n has a reduced QR-decomposition
  • · Replies 4 ·
Replies
4
Views
4K