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Linear and Abstract Algebra Forum

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.

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Proof: Nilpotent Matrix A & Real Matrices AB-BA=I

Feb 2, 2007 · Replies 2 · Feb 2, 2007

Replies: 2

Views: 3K

Does one zero equal its algebraic conjugate?

Feb 1, 2007 · Replies 2 · Feb 1, 2007

Replies: 2

Views: 3K

A different approach to prime numbers

Jan 31, 2007 · Replies 3 · Feb 1, 2007

Replies: 3

Views: 4K

Inverses of Units: Are All Conjugates Always in the Field?

Jan 8, 2007 · Replies 1 · Feb 1, 2007

Replies: 1

Views: 2K

How Do Groups Relate to Symmetry in Mathematics?

Jan 28, 2007 · Replies 6 · Jan 31, 2007

Replies: 6

Views: 4K

Matrix Variables: Solving Mx = b with 2-D Vectors

Jan 29, 2007 · Replies 2 · Jan 29, 2007

Replies: 2

Views: 2K

Understanding Vector Spaces in Linear Algebra

Jan 29, 2007 · Replies 2 · Jan 29, 2007

Replies: 2

Views: 2K

Question related to Pell's Equation

Nov 21, 2006 · Replies 7 · Jan 29, 2007

Replies: 7

Views: 3K

Finding the Limit of a Fibonacci Series

Jan 24, 2007 · Replies 9 · Jan 25, 2007

Replies: 9

Views: 8K

Why the prime/irreducible distinction?

Jan 14, 2007 · Replies 12 · Jan 25, 2007

Replies: 12

Views: 7K

Spanning sets, and linear independence of them

Jan 24, 2007 · Replies 5 · Jan 24, 2007

Replies: 5

Views: 11K

Discovering Pairs of Positive Integers for Divisibility Puzzle

Jan 24, 2007 · Replies 1 · Jan 24, 2007

Replies: 1

Views: 3K

Automorphisms and some maps that are bijective

Jan 23, 2007 · Replies 2 · Jan 23, 2007

Replies: 2

Views: 2K

What are the components of an isometry in Euclidean space?

Jan 23, 2007 · Replies 2 · Jan 23, 2007

Replies: 2

Views: 2K

What Does 'Canonical' Mean in Mathematics?

Jan 16, 2007 · Replies 9 · Jan 23, 2007

Replies: 9

Views: 12K

Meaning of 'Space': Vector, Banach & Set Definitions

Jan 22, 2007 · Replies 3 · Jan 22, 2007

Replies: 3

Views: 3K

How can I prove that W contains all elementary matrices?

Jan 20, 2007 · Replies 8 · Jan 22, 2007

Replies: 8

Views: 4K

Proving n & m Divide k When gcd(m,n)=1

Jan 19, 2007 · Replies 3 · Jan 19, 2007

Replies: 3

Views: 3K

Understanding Vector Spaces and Subspaces

Dec 2, 2006 · Replies 16 · Jan 18, 2007

Replies: 16

Views: 5K

Approximate evaluation of this series (exponential sum)

Jan 13, 2007 · Replies 7 · Jan 17, 2007

Replies: 7

Views: 9K

Proving B is Involutory if A is Idempotent

Jan 16, 2007 · Replies 2 · Jan 16, 2007

Replies: 2

Views: 3K

A quick Question about the set of Automorphisms of a field F

Jan 6, 2007 · Replies 8 · Jan 10, 2007

Replies: 8

Views: 3K

Forward difference Newtons formula

Jan 9, 2007 · Replies 1 · Jan 10, 2007

Replies: 1

Views: 3K

Nonlinear Characters and Finite Groups: A Case Study

Jan 9, 2007 · Replies 1 · Jan 9, 2007

Replies: 1

Views: 4K

Proof of Roots of Unity: Solving a Missing Step

Jan 8, 2007 · Replies 2 · Jan 8, 2007

Replies: 2

Views: 5K

Characters of Normal Subgroup of Index 2

Jan 7, 2007 · Replies 3 · Jan 8, 2007

Replies: 3

Views: 5K

Characteristic Polynomial for A with a=-1

Jan 5, 2007 · Replies 3 · Jan 7, 2007

Replies: 3

Views: 3K

Inner Product: Equation for x^p & x^q | 65 Chars

Jan 5, 2007 · Replies 3 · Jan 5, 2007

Replies: 3

Views: 3K

Is Fermat's Last Theorem Still Unsolvable in Base n?

Jan 2, 2007 · Replies 1 · Jan 2, 2007

Replies: 1

Views: 4K

Wythoff' array and Wechsler's Sequence

Dec 25, 2006 · Replies 2 · Jan 2, 2007

Replies: 2

Views: 3K

Dimensions Clarification needed.

Dec 24, 2006 · Replies 17 · Jan 1, 2007

Replies: 17

Views: 4K

How Can a New Basis Change the Matrix Representation of a Linear Transformation?

Dec 17, 2006 · Replies 1 · Dec 31, 2006

Replies: 1

Views: 7K

Is Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))?

Dec 29, 2006 · Replies 7 · Dec 30, 2006

Replies: 7

Views: 4K

Proving Subgroups of Free Abelian Groups: A Troubleshooting Guide

Dec 25, 2006 · Replies 4 · Dec 30, 2006

Replies: 4

Views: 8K

Stationarity Theory: Math Overview

Dec 25, 2006 · Replies 1 · Dec 29, 2006

Replies: 1

Views: 2K

What a representation of a group is please?

Oct 2, 2005 · Replies 25 · Dec 29, 2006

Replies: 25

Views: 5K

Vector spaces over fields other than R or C?

Dec 28, 2006 · Replies 4 · Dec 28, 2006

Replies: 4

Views: 4K

Difference between algebra and module?

Dec 22, 2006 · Replies 6 · Dec 27, 2006

Replies: 6

Views: 10K

Solving simultaneous trigonometric equations

Dec 17, 2006 · Replies 6 · Dec 26, 2006

Replies: 6

Views: 25K

Understanding the Role of Quaternions: Algebra, Normed Linear Space, and Field

Dec 23, 2006 · Replies 2 · Dec 23, 2006

Replies: 2

Views: 3K

Proving the Equality of Rank for Finitely Generated Ideals in Number Fields

Dec 23, 2006 · Replies 21 · Dec 23, 2006

Replies: 21

Views: 5K

One more elementary question, on square roots

Dec 22, 2006 · Replies 3 · Dec 23, 2006

Replies: 3

Views: 3K

Clifford algebra isomorphic to tensor algebra or exterior algebra?

Dec 22, 2006 · Replies 2 · Dec 23, 2006

Replies: 2

Views: 12K

Lucas-Lehmer Test With Polynomials

Dec 3, 2006 · Replies 2 · Dec 22, 2006

Replies: 2

Views: 3K

What is a Graded Algebra with Z_2 Grading?

Dec 21, 2006 · Replies 5 · Dec 22, 2006

Replies: 5

Views: 8K

Is There a Square of a Rational Number Between Any Two Positive Rationals?

Dec 19, 2006 · Replies 5 · Dec 22, 2006

Replies: 5

Views: 3K

Efficiently Calculating Determinants Using Cofactors and Expansion

Dec 15, 2006 · Replies 10 · Dec 19, 2006

Replies: 10

Views: 3K

How can primorials be used to generate a sequence of prime numbers?

Oct 16, 2006 · Replies 9 · Dec 19, 2006

Replies: 9

Views: 4K

Explaining Non Archimedean Norm Proof

Dec 18, 2006 · Replies 2 · Dec 18, 2006

Replies: 2

Views: 4K

Hiding small numbers in a huge number?

Dec 16, 2006 · Replies 4 · Dec 17, 2006

Replies: 4

Views: 3K

What are some key results in algebraic number theory and how can they be proven?

Oct 18, 2006 · Replies 12 · Dec 16, 2006

Replies: 12

Views: 4K

How to prove trace(A.A*) is positive

Dec 14, 2006 · Replies 4 · Dec 15, 2006

Replies: 4

Views: 7K

Conflict of interests results in lies?

Dec 14, 2006 · Replies 2 · Dec 14, 2006

Replies: 2

Views: 2K

Are There Geometrical Methods to Find Integer Points for 2D Symmetryc Form?

Nov 24, 2006 · Replies 9 · Dec 14, 2006

Replies: 9

Views: 4K

Definition of Simultaneous Linear Difference Equations

Dec 13, 2006 · Replies 3 · Dec 13, 2006

Replies: 3

Views: 4K

How can I solve the parametric representation problem for x^3+y^3=u^3+v^3?

Dec 11, 2006 · Replies 2 · Dec 12, 2006

Replies: 2

Views: 3K

Polynomials and the Inner Product

Dec 11, 2006 · Replies 14 · Dec 11, 2006

Replies: 14

Views: 10K

How Does SL(2,C) Relate to Its Manifold Structure?

Dec 7, 2006 · Replies 3 · Dec 11, 2006

Replies: 3

Views: 2K

Cyclotomic polynomials and primitive roots of unity

Dec 4, 2006 · Replies 4 · Dec 10, 2006

Replies: 4

Views: 9K

Help with Final Exam Questions: QUESTION TWO (b) & SIX (a)

Dec 9, 2006 · Replies 9 · Dec 10, 2006

Replies: 9

Views: 4K

Randomness of digits of irrational numbers.

Dec 9, 2006 · Replies 2 · Dec 9, 2006

Replies: 2

Views: 6K

A little problem involving unitary matrices

Sep 19, 2006 · Replies 6 · Dec 7, 2006

Replies: 6

Views: 3K

Issue regarding the orthogonality of eigenvectors for Hermitian

Feb 18, 2006 · Replies 20 · Dec 7, 2006

Replies: 20

Views: 5K

Understanding Ring Embeddings and Irreducible Polynomials: Questions Answered

Nov 21, 2006 · Replies 5 · Dec 6, 2006

Replies: 5

Views: 2K

Are Normal Subgroups Defined by Equality of Left and Right Cosets?

Dec 5, 2006 · Replies 3 · Dec 6, 2006

Replies: 3

Views: 4K

Can Unique Subgroups Be Generalized as Normal Subgroups?

Dec 5, 2006 · Replies 1 · Dec 5, 2006

Replies: 1

Views: 2K

MOdular Hypergeometric Sieve and Parallel Processing

Dec 2, 2006 · Replies 5 · Dec 3, 2006

Replies: 5

Views: 3K

How Do I Solve This Linear Algebra Equation?

Dec 2, 2006 · Replies 3 · Dec 3, 2006

Replies: 3

Views: 3K

Are there any non-trivial automorphisms of the field Q(sqrt2)?

Nov 25, 2006 · Replies 8 · Nov 30, 2006

Replies: 8

Views: 5K

TI89 Simplex Method LP Solver: Phase 1 & 2 Pivoting

Nov 28, 2006 · Replies 2 · Nov 28, 2006

Replies: 2

Views: 3K

How to Solve Complex Eigenvectors in Matrix Algebra

Nov 27, 2006 · Replies 1 · Nov 28, 2006

Replies: 1

Views: 7K

How Does Lagrange's Theorem Prove a^(|G|+1) = a in Finite Groups?

Nov 22, 2006 · Replies 10 · Nov 24, 2006

Replies: 10

Views: 2K

Is Number Theory a Challenging and Rewarding Course?

Nov 13, 2006 · Replies 9 · Nov 24, 2006

Replies: 9

Views: 4K

B.D: Proving C_m^+ in Lucas-Lehmer Test (LLT)

Nov 19, 2006 · Replies 11 · Nov 23, 2006

Replies: 11

Views: 3K

Newton (iterative) method to solve a diophantine equation

Nov 2, 2006 · Replies 5 · Nov 23, 2006

Replies: 5

Views: 6K

Exploring Irreducible Polynomial and Reducing Techniques for g(x)

Oct 31, 2006 · Replies 4 · Nov 22, 2006

Replies: 4

Views: 3K

How does the Linear Spike Method relate phi(x,y) to pi(N)?

Nov 21, 2006 · Replies 4 · Nov 22, 2006

Replies: 4

Views: 4K

Proving Norm Difference in Euclidean Ring Z[{\sqrt 2 \over 2}(1+i)]

Nov 21, 2006 · Replies 9 · Nov 22, 2006

Replies: 9

Views: 3K

Euclidean Ring of Z[\zeta]: Unconventional Technique

Nov 21, 2006 · Replies 2 · Nov 21, 2006

Replies: 2

Views: 3K

Understanding Linear Transformations and Their Applications in Vector Spaces

Nov 17, 2006 · Replies 8 · Nov 21, 2006

Replies: 8

Views: 3K

Understanding FLT: Debunking the Myth of Simple Solutions

Jul 5, 2005 · Replies 28 · Nov 21, 2006

Replies: 28

Views: 6K

Calculating JNF & Basis Vectors: Jordan Normal Form

Nov 18, 2006 · Replies 2 · Nov 20, 2006

Replies: 2

Views: 5K

Vector space for cross products?

Nov 18, 2006 · Replies 3 · Nov 19, 2006

Replies: 3

Views: 4K

Possible Non-negative Integer Solutions to 3^x + 5^y = 7^z + 1

Nov 10, 2006 · Replies 6 · Nov 19, 2006

Replies: 6

Views: 3K

Where Can I Find Abstract Algebra Problems for Studying the Math GRE?

Nov 12, 2006 · Replies 9 · Nov 18, 2006

Replies: 9

Views: 5K

Need help with vectors, angles, etc please

Nov 17, 2006 · Replies 2 · Nov 18, 2006

Replies: 2

Views: 2K

Converting from 2D coordinate Systems

Nov 17, 2006 · Replies 1 · Nov 18, 2006

Replies: 1

Views: 5K

Can a Differential Equation Describe the Prime Counting Function?

Aug 7, 2006 · Replies 5 · Nov 18, 2006

Replies: 5

Views: 6K

Hints that a dynamical system may lie behind the distribution of primes

Oct 30, 2006 · Replies 7 · Nov 17, 2006

Replies: 7

Views: 3K

Linearly Independent Vectors: Same Plane?

Nov 16, 2006 · Replies 2 · Nov 16, 2006

Replies: 2

Views: 2K

A quick question on coefficient of binomial expansion

Oct 31, 2006 · Replies 7 · Nov 16, 2006

Replies: 7

Views: 7K

What is the Unique Function Possessing Certain Properties on Positive Integers?

Oct 29, 2006 · Replies 11 · Nov 16, 2006

Replies: 11

Views: 4K

Show Existence of Basis for Vector Space V with No Elements from Subspace M

Nov 14, 2006 · Replies 7 · Nov 15, 2006

Replies: 7

Views: 3K

Polynomial Multiplication with NTT

Oct 28, 2006 · Replies 8 · Nov 15, 2006

Replies: 8

Views: 8K

Elements in only 1 left/right coset

Nov 14, 2006 · Replies 2 · Nov 15, 2006

Replies: 2

Views: 2K

Does an Extension of the Primorial Function Exist?

Oct 17, 2006 · Replies 3 · Nov 13, 2006

Replies: 3

Views: 3K

Linear representations in Char 0

Nov 12, 2006 · Replies 1 · Nov 12, 2006

Replies: 1

Views: 3K

A real number definition involving Bruijn-Newmann constant

Nov 8, 2006 · Replies 6 · Nov 11, 2006

Replies: 6

Views: 5K

Understanding Vector Quotient Spaces in Linear Algebra

Nov 10, 2006 · Replies 8 · Nov 10, 2006

Replies: 8

Views: 4K

Questions on Free Products II: Subgroup of Normal & Amalgamated

Oct 31, 2006 · Replies 16 · Nov 9, 2006

Replies: 16

Views: 3K

Linear and Abstract Algebra

Linear and abstract algebra are branches of mathematics that deal with algebraic structures and their properties.

Linear algebra primarily focuses on vector spaces, linear transformations, and systems of linear equations. It provides essential tools for understanding geometric concepts, solving linear equations, and working with matrices. Abstract algebra, on the other hand, is a more generalized study that investigates algebraic structures such as groups, rings, and fields. It delves into the properties and relationships of algebraic systems, aiming to identify common structures and abstract patterns.

Both linear and abstract algebra are foundational areas of mathematics with applications spanning diverse fields, from physics and computer science to cryptography and optimization.

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