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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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Diagonalizability (in Hilbert Spaces)

Mar 13, 2006 · Replies 11 · Apr 19, 2006

Replies: 11

Views: 5K

What,s the meaning of this expression?

Apr 15, 2006 · Replies 3 · Apr 15, 2006

Replies: 3

Views: 3K

? about Godel's incomplete theorm

Apr 11, 2006 · Replies 5 · Apr 11, 2006

Replies: 5

Views: 3K

What is the Justification for the Conjecture on Intuitive Number Theory?

Mar 22, 2006 · Replies 5 · Apr 10, 2006

Replies: 5

Views: 5K

Group Extensions: A Simple Guide

Apr 10, 2006 · Replies 2 · Apr 10, 2006

Replies: 2

Views: 3K

Suppose there is a cube and we can colour the cube's faces

Apr 8, 2006 · Replies 4 · Apr 10, 2006

Replies: 4

Views: 2K

Last Digit of 3^999: Solving the Puzzle

Mar 31, 2006 · Replies 8 · Apr 9, 2006

Replies: 8

Views: 20K

Probability of [log₁₀(4x)]-[log₁₀(x)]=0 for x (0,1)

Apr 6, 2006 · Replies 2 · Apr 8, 2006

Replies: 2

Views: 2K

Can Cosine or Sine Values be Expressed Using Roots of Rationals?

Apr 6, 2006 · Replies 1 · Apr 7, 2006

Replies: 1

Views: 3K

How much calculus in linear algebra?

Apr 5, 2006 · Replies 5 · Apr 6, 2006

Replies: 5

Views: 4K

Finding the Intersection of Subspaces with Given Spanning Vectors

Apr 5, 2006 · Replies 2 · Apr 5, 2006

Replies: 2

Views: 9K

Proposition 36 of book IX in the elements

Mar 31, 2006 · Replies 2 · Apr 4, 2006

Replies: 2

Views: 3K

HIlbert-Polya conjecture ¿proof or RH?

Apr 3, 2006 · Replies 2 · Apr 3, 2006

Replies: 2

Views: 10K

Proof for nonexistence of a prime counting function?

Mar 22, 2006 · Replies 21 · Apr 3, 2006

Replies: 21

Views: 7K

Inference of even or odd from the number of divisors?

Mar 31, 2006 · Replies 4 · Apr 2, 2006

Replies: 4

Views: 4K

Can the Lebesgue Integral of a_p be Defined for Non-Differentiable Functions?

Mar 24, 2006 · Replies 8 · Apr 2, 2006

Replies: 8

Views: 3K

Solve k^2-1=a^2+b^2: Find Positive Ints

Mar 19, 2006 · Replies 7 · Mar 30, 2006

Replies: 7

Views: 2K

Can we prove linear independence with just matrix and vector information?

Mar 28, 2006 · Replies 3 · Mar 29, 2006

Replies: 3

Views: 3K

Article: Prime Numbers Get Hitched

Mar 28, 2006 · Replies 6 · Mar 28, 2006

Replies: 6

Views: 3K

Abstract Algebra: Applications & Overview

Dec 29, 2005 · Replies 21 · Mar 28, 2006

Replies: 21

Views: 8K

Can Your Insights on Primes Unlock the Riemann Hypothesis?

Mar 8, 2006 · Replies 53 · Mar 26, 2006

2

Replies: 53

Views: 12K

Composite numbers and squares from recursive series

Mar 9, 2006 · Replies 6 · Mar 24, 2006

Replies: 6

Views: 4K

Non-Negative Integer Binary Concatenation: Is This an Irrational Number?

Mar 21, 2006 · Replies 15 · Mar 24, 2006

Replies: 15

Views: 3K

Linear Independence and Dependence in C^d: Questions from Abbas Edalat's Notes

Mar 21, 2006 · Replies 4 · Mar 22, 2006

Replies: 4

Views: 4K

Understanding Orthogonal Projection in Linear Operators

Mar 18, 2006 · Replies 8 · Mar 20, 2006

Replies: 8

Views: 8K

How to prove normality of a field extension with Q(\sqrt{2+\sqrt{2}}):Q?

Mar 15, 2006 · Replies 35 · Mar 19, 2006

2

Replies: 35

Views: 9K

Struggling with Linear Algebra? Need more practice problems and answers?

Mar 17, 2006 · Replies 7 · Mar 19, 2006

Replies: 7

Views: 14K

Inconsistent Inner Product Definitions

Mar 18, 2006 · Replies 1 · Mar 18, 2006

Replies: 1

Views: 3K

Finding Roots and Order of an Integer: Two Problems in Number Theory

Mar 14, 2006 · Replies 3 · Mar 15, 2006

Replies: 3

Views: 5K

Best Number Theory Books for Self Study | Ogilvy & Hardy

Mar 1, 2006 · Replies 6 · Mar 15, 2006

Replies: 6

Views: 4K

What Are Primitive Roots and Why Are They Important?

Mar 13, 2006 · Replies 5 · Mar 14, 2006

Replies: 5

Views: 10K

What is the level of difficulty in understanding Gregory Chaitin's Meta Math?

Feb 24, 2006 · Replies 5 · Mar 14, 2006

Replies: 5

Views: 4K

Are Alternative Prime Sequences Easier to Predict Than Traditional Primes?

Mar 12, 2006 · Replies 17 · Mar 14, 2006

Replies: 17

Views: 4K

Why is the 2-norm of A^k equal to 2-norm of T^k?

Mar 13, 2006 · Replies 2 · Mar 14, 2006

Replies: 2

Views: 2K

Is .99 Repeating Truly Equal to 1?

Feb 13, 2006 · Replies 11 · Mar 13, 2006

Replies: 11

Views: 5K

Calculating Pi: Find Reliable Measurments

Mar 13, 2006 · Replies 3 · Mar 13, 2006

Replies: 3

Views: 3K

A problem like Fermat's Last Theorem

Mar 11, 2006 · Replies 15 · Mar 12, 2006

Replies: 15

Views: 5K

Is Conjugate Symmetry Enough for a Hermitian Inner Product?

Mar 11, 2006 · Replies 2 · Mar 11, 2006

Replies: 2

Views: 6K

How to Solve Group Theory Problems and Understand Underlying Concepts?

Mar 7, 2006 · Replies 4 · Mar 10, 2006

Replies: 4

Views: 4K

Solve a^2 + b^2 = c^3: Integer Solutions

Mar 8, 2006 · Replies 8 · Mar 10, 2006

Replies: 8

Views: 3K

Does the Limit of Unioned Fractions Equal the Rationals in [0,1]?

Oct 23, 2005 · Replies 26 · Mar 8, 2006

Replies: 26

Views: 6K

Can Anyone Help with These RSA Encryption Questions?

Mar 7, 2006 · Replies 1 · Mar 7, 2006

Replies: 1

Views: 6K

Linear Algebra Texts Recommended for Rigorous Approach

Nov 25, 2004 · Replies 47 · Mar 7, 2006

2

Replies: 47

Views: 11K

Ring Theory: Introduction and Beyond

Mar 6, 2006 · Replies 3 · Mar 7, 2006

Replies: 3

Views: 5K

Sylow first thm and normal subgroups

Feb 28, 2006 · Replies 10 · Mar 2, 2006

Replies: 10

Views: 4K

Classify all groups of order 147

Mar 1, 2006 · Replies 4 · Mar 2, 2006

Replies: 4

Views: 5K

How many possible menus can be created with 10 foods from 4 categories?

Mar 1, 2006 · Replies 2 · Mar 1, 2006

Replies: 2

Views: 3K

Discovering Perfect Squares in x!+1 Function | Roger's Experience and Insights

Mar 1, 2006 · Replies 10 · Mar 1, 2006

Replies: 10

Views: 5K

What can I expect from a course in Abstract Linear Algebra?

Feb 27, 2006 · Replies 3 · Feb 28, 2006

Replies: 3

Views: 6K

Does the Addition of Subspaces Always Result in Unique Additive Identities?

Feb 23, 2006 · Replies 17 · Feb 27, 2006

Replies: 17

Views: 5K

Algorithmic complexity of primes

Feb 27, 2006 · Replies 1 · Feb 27, 2006

Replies: 1

Views: 3K

Explaining Minimal Polynomial of Matrix A

Feb 23, 2006 · Replies 10 · Feb 25, 2006

Replies: 10

Views: 5K

How Is the Primary Decomposition Theorem Known in Various Mathematical Texts?

Feb 24, 2006 · Replies 3 · Feb 24, 2006

Replies: 3

Views: 7K

Group Theory Textbooks: Recommended Books & Numerical Examples

Feb 22, 2006 · Replies 8 · Feb 23, 2006

Replies: 8

Views: 5K

Proving Functions: The Relationship Between Onto and 1-to-1 Properties

Feb 21, 2006 · Replies 7 · Feb 22, 2006

Replies: 7

Views: 3K

Space Complexity of Number-theoretic Algorithms

Feb 15, 2006 · Replies 8 · Feb 21, 2006

Replies: 8

Views: 7K

Proofs of Group Theory for Theoretical Physicists - Daniel

Feb 20, 2006 · Replies 1 · Feb 20, 2006

Replies: 1

Views: 4K

Is Lambda an Eigenvalue of A in the Cayley-Hamilton Theorem Proof?

Feb 14, 2006 · Replies 7 · Feb 18, 2006

Replies: 7

Views: 9K

Coding theory & cryptography books

Jan 24, 2006 · Replies 3 · Feb 16, 2006

Replies: 3

Views: 5K

Prime Number Multiplication: Is Result Always Prime?

Jan 5, 2006 · Replies 17 · Feb 15, 2006

Replies: 17

Views: 5K

Understanding Transcendal Numbers: Importance and Examples

Feb 15, 2006 · Replies 5 · Feb 15, 2006

Replies: 5

Views: 3K

Towers of integers and divisibilty by 11

Feb 5, 2006 · Replies 9 · Feb 8, 2006

Replies: 9

Views: 3K

Is it Valid to Use Congruences to Show No Solution for Fermat's Last Theorem?

Feb 7, 2006 · Replies 4 · Feb 7, 2006

Replies: 4

Views: 4K

Is the Inverse of a Diagonal Matrix Simply the Inverse of Its Elements?

Jan 26, 2006 · Replies 3 · Feb 6, 2006

Replies: 3

Views: 19K

Understanding Null Space: A Plain English Guide

Jan 26, 2006 · Replies 8 · Feb 6, 2006

Replies: 8

Views: 6K

I was reading simon singh's the code book

Jan 2, 2006 · Replies 7 · Feb 6, 2006

Replies: 7

Views: 5K

Non integer square roots and pi = irrational?

Dec 21, 2005 · Replies 54 · Feb 5, 2006

2

Replies: 54

Views: 16K

How Is Symmetric Algebra Isomorphic to a Free Commutative R-Algebra?

Feb 4, 2006 · Replies 2 · Feb 4, 2006

Replies: 2

Views: 3K

Infinite number of open intervals

Feb 1, 2006 · Replies 18 · Feb 4, 2006

Replies: 18

Views: 5K

Max Trace of U(N) Matrices: A Complex Problem

Feb 3, 2006 · Replies 1 · Feb 3, 2006

Replies: 1

Views: 2K

Proof of the Left Distributive Law for matrices.

Jan 30, 2006 · Replies 3 · Feb 1, 2006

Replies: 3

Views: 24K

Ancient puzzle, solved by abstract algebra?

Jan 22, 2006 · Replies 3 · Jan 29, 2006

Replies: 3

Views: 3K

Is $\forall p,q,r \in \mathbb{N}$ Satisfiable?

Nov 29, 2005 · Replies 11 · Jan 27, 2006

Replies: 11

Views: 4K

What are T2-Spaces and Separability in Topology?

Jan 13, 2006 · Replies 44 · Jan 26, 2006

2

Replies: 44

Views: 11K

How Do You Construct a [4, 7^2, 3] Code Using MOLS?

Jan 22, 2006 · Replies 4 · Jan 26, 2006

Replies: 4

Views: 3K

Is Representation Theory on Rigged Hilbert Spaces Explored in Textbooks?

Jan 12, 2006 · Replies 1 · Jan 25, 2006

Replies: 1

Views: 3K

How does one compute the number of ring homomorphisms

Jan 23, 2006 · Replies 3 · Jan 24, 2006

Replies: 3

Views: 2K

Understanding Notation and Proving Linear Independence

Jan 22, 2006 · Replies 2 · Jan 23, 2006

Replies: 2

Views: 4K

Applications of singular matricies

Jan 21, 2006 · Replies 2 · Jan 21, 2006

Replies: 2

Views: 3K

Vector Products: What Happens When Professors Refuse to Explain?

Jan 20, 2006 · Replies 4 · Jan 21, 2006

Replies: 4

Views: 3K

Solving Generating Function Problems - How to Get the Answer

Jan 16, 2006 · Replies 7 · Jan 19, 2006

Replies: 7

Views: 4K

Completing the Spinor Group Commutative Diagram

Jan 18, 2006 · Replies 1 · Jan 18, 2006

Replies: 1

Views: 3K

Division by Seven and Modular Arithmetic: The Ultimate Guide

Jan 13, 2006 · Replies 12 · Jan 16, 2006

Replies: 12

Views: 4K

What is the Definition of Moduli of Elasticity?

Jan 14, 2006 · Replies 17 · Jan 14, 2006

Replies: 17

Views: 51K

Digitized Proof of Wiles' Fermat's Last Theorem: Seeking a Link | Neohaven

Jan 13, 2006 · Replies 2 · Jan 13, 2006

Replies: 2

Views: 3K

How Do Factors Relate in the Quadratic Form N^2 - 3N + 1?

Jan 12, 2006 · Replies 2 · Jan 12, 2006

Replies: 2

Views: 3K

What Does [\mathcal{L},\mathcal{L}] = \mathcal{L} Imply in Simple Lie Algebras?

Dec 30, 2005 · Replies 29 · Jan 11, 2006

Replies: 29

Views: 6K

Endomorphism Compositions and Injectivity/Surjectivity Criteria for Groups

Sep 25, 2005 · Replies 4 · Jan 9, 2006

Replies: 4

Views: 3K

M43: GIMPS project has found a new Mersenne prime

Dec 31, 2005 · Replies 15 · Jan 9, 2006

Replies: 15

Views: 4K

Linear algebra proof definition of a stochastic matrix

Jan 7, 2006 · Replies 2 · Jan 7, 2006

Replies: 2

Views: 9K

6 generals propose locking a safe with a number of different locks

Nov 30, 2005 · Replies 2 · Jan 2, 2006

Replies: 2

Views: 3K

Is It Possible to Identify an Original Isomorphism in Group Theory?

Dec 16, 2005 · Replies 16 · Dec 21, 2005

Replies: 16

Views: 3K

Counting Primitive Roots in Finite Fields without Group Theory

Dec 16, 2005 · Replies 10 · Dec 20, 2005

Replies: 10

Views: 5K

How Do You Rotate a Complex Number by 270 Degrees?

Dec 17, 2005 · Replies 5 · Dec 19, 2005

Replies: 5

Views: 5K

Fourier complex series for Pi(x)

Dec 12, 2005 · Replies 16 · Dec 19, 2005

Replies: 16

Views: 7K

Applications of Algebra: Groups, Rings, Ideals

Dec 17, 2005 · Replies 1 · Dec 17, 2005

Replies: 1

Views: 3K

Can You Prove the Sum of Cubes Equals the Square of the Sum?

Dec 15, 2005 · Replies 4 · Dec 16, 2005

Replies: 4

Views: 3K

FLT-Solution for prime values of n .

Dec 5, 2005 · Replies 22 · Dec 15, 2005

Replies: 22

Views: 4K

Subspaces, R^n How to visualize?

Dec 11, 2005 · Replies 7 · Dec 12, 2005

Replies: 7

Views: 3K

Infinite primes using Quadratic Residues

Dec 11, 2005 · Replies 1 · Dec 12, 2005

Replies: 1

Views: 4K

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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