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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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Understanding x=pmodn: An Integer Modular Arithmetic Primer

Mar 5, 2004 · Replies 2 · Mar 6, 2004

Replies: 2

Views: 3K

Can recursive square roots reveal the secrets of the golden ratio?

Mar 1, 2004 · Replies 12 · Mar 4, 2004

Replies: 12

Views: 9K

Extended Fermat's last theorem.

Mar 2, 2004 · Replies 7 · Mar 4, 2004

Replies: 7

Views: 4K

Proof of the formula for the nth derivative of a product

Feb 12, 2004 · Replies 18 · Mar 3, 2004

Replies: 18

Views: 15K

How Do I Proceed with Variable Row Reduction?

Feb 24, 2004 · Replies 2 · Mar 2, 2004

Replies: 2

Views: 3K

A partial solution to the Goldbach Conjecture

Mar 1, 2004 · Replies 7 · Mar 2, 2004

Replies: 7

Views: 6K

Can you easily invert 3 by 3 matrices using a simple formula?

Dec 20, 2003 · Replies 9 · Mar 2, 2004

Replies: 9

Views: 6K

How Does Two-Digit Counting Work Across Different Number Bases?

Feb 25, 2004 · Replies 8 · Mar 1, 2004

Replies: 8

Views: 11K

Discovering Primes: The Relationship Between p and 2p + 2

Feb 25, 2004 · Replies 18 · Feb 29, 2004

Replies: 18

Views: 4K

Understanding the Cross Product of Vectors: Perpendicular Properties Explained

Nov 30, 2003 · Replies 42 · Feb 27, 2004

2

Replies: 42

Views: 25K

Discovering a Simple Inequality for Divisor Count in Positive Integers

Feb 19, 2004 · Replies 2 · Feb 26, 2004

Replies: 2

Views: 3K

Searching for Perfect Squares using the Pythagorean Theorem

Feb 3, 2004 · Replies 2 · Feb 24, 2004

Replies: 2

Views: 3K

Understanding Irrational Numbers: Is it Possible to Exact Measure?

Feb 18, 2004 · Replies 4 · Feb 22, 2004

Replies: 4

Views: 4K

Solving Simultaneous Equations for Confused Students

Feb 20, 2004 · Replies 9 · Feb 21, 2004

Replies: 9

Views: 3K

Find a linear differentiation transformation

Feb 18, 2004 · Replies 5 · Feb 20, 2004

Replies: 5

Views: 7K

Multiplication=addition 2*2=2+2=4

Feb 12, 2004 · Replies 12 · Feb 19, 2004

Replies: 12

Views: 4K

Is A invertible if {v1, v2} and {Av1, Av2} are linearly independent sets?

Feb 12, 2004 · Replies 2 · Feb 19, 2004

Replies: 2

Views: 3K

Coefficient of Friction: What is the Equation?

Feb 10, 2004 · Replies 2 · Feb 18, 2004

Replies: 2

Views: 3K

What are Isomorphisms: A Beginner's Guide to Understanding Algebraic Structures.

Feb 12, 2004 · Replies 10 · Feb 15, 2004

Replies: 10

Views: 7K

Has the Prime Number Distribution Puzzle Been Cracked?

Sep 29, 2003 · Replies 33 · Feb 14, 2004

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Replies: 33

Views: 11K

Proving Properties of Exponents Using Induction

Feb 10, 2004 · Replies 3 · Feb 11, 2004

Replies: 3

Views: 3K

Proving n! > n^2 for n ≥ 4 with Induction

Feb 3, 2004 · Replies 2 · Feb 10, 2004

Replies: 2

Views: 2K

Clifford Algebra Question on Vectors

Feb 6, 2004 · Replies 5 · Feb 9, 2004

Replies: 5

Views: 3K

Has Any One solved Fermats Last Theorem ?

Feb 8, 2004 · Replies 6 · Feb 9, 2004

Replies: 6

Views: 5K

Vector Spaces and polynomial functions

Feb 7, 2004 · Replies 15 · Feb 8, 2004

Replies: 15

Views: 9K

Growth of Functions - What is "Log Star" (O(log*n))?

Feb 7, 2004 · Replies 5 · Feb 7, 2004

Replies: 5

Views: 5K

Vector Transformation in \mathbb{R}^n and \mathbb{R}^m with Separable Components

Jan 31, 2004 · Replies 2 · Feb 7, 2004

Replies: 2

Views: 11K

Algebraic closure of finite field

Feb 5, 2004 · Replies 9 · Feb 6, 2004

Replies: 9

Views: 9K

Proving n^3>n^2: Using Mathematical Induction and Set of Natural Numbers

Feb 6, 2004 · Replies 3 · Feb 6, 2004

Replies: 3

Views: 3K

Is zero considered a number in mathematics?

Nov 21, 2003 · Replies 33 · Feb 5, 2004

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Replies: 33

Views: 7K

Solving Polynomial Equations: Help With (x+3)^2/3=3 & 1-1=3

Feb 4, 2004 · Replies 2 · Feb 5, 2004

Replies: 2

Views: 3K

Goldbach Conjecture: Proving the Theory

Sep 21, 2003 · Replies 20 · Feb 4, 2004

Replies: 20

Views: 9K

Proofs: If a|b then -a|b, a|-b, -a|-ab

Feb 3, 2004 · Replies 4 · Feb 4, 2004

Replies: 4

Views: 5K

Solving Linear Systems: 14" Hemlock & 8" Blue Spruce

Jan 23, 2004 · Replies 3 · Feb 3, 2004

Replies: 3

Views: 4K

How Can I Prove |ab| = |ba| in a Group?

Feb 2, 2004 · Replies 7 · Feb 3, 2004

Replies: 7

Views: 6K

Is 1 a Prime Number? - Fact Check

Feb 1, 2004 · Replies 3 · Feb 2, 2004

Replies: 3

Views: 4K

Proving that gcd(x, n) = gcd(n-x, n) for 0 ≤ x ≤ n/2

Jan 31, 2004 · Replies 5 · Feb 2, 2004

Replies: 5

Views: 4K

How Do You Prove the Order of ab is mn in an Abelian Group When gcd(m, n) = 1?

Jan 29, 2004 · Replies 5 · Jan 30, 2004

Replies: 5

Views: 10K

Help with Proof: Prove n \equiv 3(mod 6) if 2^n + n^2 is Prime

Jan 22, 2004 · Replies 2 · Jan 30, 2004

Replies: 2

Views: 3K

What Makes the Number 9 So Mysterious and Fascinating?

Nov 25, 2003 · Replies 13 · Jan 27, 2004

Replies: 13

Views: 6K

Another proof I have a question about

Jan 25, 2004 · Replies 4 · Jan 25, 2004

Replies: 4

Views: 3K

Proving the Distributive Law for Integers

Jan 21, 2004 · Replies 9 · Jan 23, 2004

Replies: 9

Views: 6K

Can You Plot the Parametrization for 3D Geometric Algebra?

Dec 13, 2003 · Replies 2 · Jan 23, 2004

Replies: 2

Views: 6K

Simple proof, just using the axioms

Jan 22, 2004 · Replies 2 · Jan 22, 2004

Replies: 2

Views: 4K

What Does 1/0 Mean and Why is It Undefined?

Nov 14, 2003 · Replies 37 · Jan 19, 2004

2

Replies: 37

Views: 10K

Semi-Direct Product: Explained in Plain English

Dec 1, 2003 · Replies 14 · Jan 17, 2004

Replies: 14

Views: 14K

What happens as we approach infinity on the number line?

Nov 26, 2003 · Replies 2 · Jan 16, 2004

Replies: 2

Views: 4K

What is the structure of group algebras for D4 and Q8?

Dec 11, 2003 · Replies 2 · Jan 16, 2004

Replies: 2

Views: 7K

What is the smallest non-solvable group and how can it be proven?

Jan 1, 2004 · Replies 6 · Jan 16, 2004

Replies: 6

Views: 8K

Klein and Cyclic Groups: Definitions and Subgroups

Jan 12, 2004 · Replies 9 · Jan 16, 2004

Replies: 9

Views: 5K

How can the parallelogram law be proven?

Jan 7, 2004 · Replies 3 · Jan 15, 2004

Replies: 3

Views: 10K

Decimal fractions and the numer 1

Dec 29, 2003 · Replies 9 · Jan 15, 2004

Replies: 9

Views: 4K

Draw Equipotential Lines & Understand Electrical Fields

Jan 9, 2004 · Replies 4 · Jan 13, 2004

Replies: 4

Views: 4K

Has the Poincare Conjecture Finally Been Solved?

Jan 1, 2004 · Replies 4 · Jan 11, 2004

Replies: 4

Views: 6K

What Are Perfect Numbers and Why Are They So Mysterious?

Nov 3, 2003 · Replies 18 · Jan 11, 2004

Replies: 18

Views: 10K

What is the relationship between a matrix A and its eigenvalue g when A-1 = A?

Jan 5, 2004 · Replies 12 · Jan 10, 2004

Replies: 12

Views: 3K

Can't solve a problem about subspaces

Jan 3, 2004 · Replies 6 · Jan 8, 2004

Replies: 6

Views: 4K

Showing 2 Lines Lie in Same Plane: Equation Solution

Jan 3, 2004 · Replies 5 · Jan 7, 2004

Replies: 5

Views: 14K

Fourier analysis of the prime distribution

Dec 13, 2003 · Replies 2 · Jan 2, 2004

Replies: 2

Views: 6K

Find the first five terms of sequence

Dec 31, 2003 · Replies 4 · Dec 31, 2003

Replies: 4

Views: 3K

Matrix Solutions and Gaussian Reduction: An Introduction to Linear Algebra

Dec 31, 2003 · Replies 4 · Dec 31, 2003

Replies: 4

Views: 13K

Finding the Transformation Matrix for Linear Transformations in R^3

Dec 29, 2003 · Replies 6 · Dec 31, 2003

Replies: 6

Views: 5K

Is Computational Number Theory Underrepresented in Online Resources?

Dec 21, 2003 · Replies 2 · Dec 29, 2003

Replies: 2

Views: 4K

Defining SO(n) and SU(n): A Search for the Right Definition

Dec 20, 2003 · Replies 2 · Dec 27, 2003

Replies: 2

Views: 3K

Trying to track down a Partition theorem

Dec 11, 2003 · Replies 2 · Dec 20, 2003

Replies: 2

Views: 3K

Greatest integer divides p^4 -1

Dec 20, 2003 · Replies 3 · Dec 20, 2003

Replies: 3

Views: 10K

Taking the logarithm of the euler product

Dec 18, 2003 · Replies 2 · Dec 18, 2003

Replies: 2

Views: 6K

Divisibility Testing for Prime Numbers

Dec 15, 2003 · Replies 7 · Dec 17, 2003

Replies: 7

Views: 5K

How can I show that y is an eigenvalue of B?

Dec 17, 2003 · Replies 3 · Dec 17, 2003

Replies: 3

Views: 6K

What makes Eigenvalues and Eigenvectors important and how were they developed?

Nov 10, 2003 · Replies 15 · Dec 16, 2003

Replies: 15

Views: 9K

Matrix A & A^t: Same Eigenvalues, Different Eigenvectors?

Dec 15, 2003 · Replies 2 · Dec 16, 2003

Replies: 2

Views: 7K

The group of invertible 2 by 2 matrices

Dec 15, 2003 · Replies 2 · Dec 15, 2003

Replies: 2

Views: 6K

Newest Prime Number Found Today!

Dec 11, 2003 · Replies 2 · Dec 14, 2003

Replies: 2

Views: 4K

Proving Linear Algebra Concepts: A=A^-1, A^T=A^-1

Dec 12, 2003 · Replies 8 · Dec 13, 2003

Replies: 8

Views: 11K

Geometric Algebra: Explaining Commutators on Tri-Vectors

Dec 10, 2003 · Replies 5 · Dec 12, 2003

Replies: 5

Views: 4K

Partitioning with Primes: Comparing P(n) and P'(n)

Dec 9, 2003 · Replies 9 · Dec 12, 2003

Replies: 9

Views: 4K

Show that if A is nonsingular symmetric matrix

Dec 2, 2003 · Replies 6 · Dec 12, 2003

Replies: 6

Views: 6K

Can I Name My Prime Series After Myself?

Dec 11, 2003 · Replies 10 · Dec 12, 2003

Replies: 10

Views: 4K

Understanding Gregory's Formula: A Mathematical Challenge

Dec 8, 2003 · Replies 8 · Dec 11, 2003

Replies: 8

Views: 8K

A query that has only got two different prime factors

Dec 2, 2003 · Replies 5 · Dec 9, 2003

Replies: 5

Views: 7K

How Is the Permutation (23) Expressed as a Product of Transpositions?

Dec 7, 2003 · Replies 4 · Dec 7, 2003

Replies: 4

Views: 9K

How can I better understand the steps of linear algebra?

Dec 6, 2003 · Replies 2 · Dec 6, 2003

Replies: 2

Views: 4K

Real primes as complex composites

Nov 26, 2003 · Replies 2 · Dec 4, 2003

Replies: 2

Views: 4K

Elementary Row Operations on Matrices

Nov 22, 2003 · Replies 3 · Dec 1, 2003

Replies: 3

Views: 21K

Benediktov Problem: Solve the Daughters' Egg Selling Challenge

Nov 22, 2003 · Replies 2 · Nov 29, 2003

Replies: 2

Views: 4K

Solving an Eigenvalue Problem for Large n Matrix

Nov 16, 2003 · Replies 5 · Nov 28, 2003

Replies: 5

Views: 4K

Is <Z_n\{0},+> a Group Without Zero?

Nov 25, 2003 · Replies 2 · Nov 25, 2003

Replies: 2

Views: 4K

How to determine if a subgroup is normal in Group Theory?

Nov 19, 2003 · Replies 6 · Nov 19, 2003

Replies: 6

Views: 6K

Logic & Algebra: F Intersect G = ?

Oct 29, 2003 · Replies 5 · Nov 17, 2003

Replies: 5

Views: 3K

Group Theory: Find the order of

Nov 11, 2003 · Replies 15 · Nov 15, 2003

Replies: 15

Views: 8K

Matrices and Matrix Calculations of Linear Algebra

Oct 4, 2003 · Replies 6 · Nov 9, 2003

Replies: 6

Views: 12K

Find A Permutation of order 6 in S5

Nov 5, 2003 · Replies 14 · Nov 6, 2003

Replies: 14

Views: 12K

Understanding Normalizing, Det/Adj & Linear Algebra

Oct 28, 2003 · Replies 2 · Nov 4, 2003

Replies: 2

Views: 7K

Raymond Smullyan's Recreational Math Paradox on Page 189: Can it be Solved?

Oct 19, 2003 · Replies 11 · Nov 2, 2003

Replies: 11

Views: 5K

Fermat's Test for Prime Numbers and Pseudo Primes: Explained

Nov 1, 2003 · Replies 8 · Nov 1, 2003

Replies: 8

Views: 5K

What is M? system of linear equations

Oct 29, 2003 · Replies 2 · Oct 29, 2003

Replies: 2

Views: 3K

Proving g2 = u in Dihedral Group of Order 8

Oct 29, 2003 · Replies 4 · Oct 29, 2003

Replies: 4

Views: 13K

Bohemian Intellectual Mathematics and Occultism

Sep 21, 2003 · Replies 1 · Oct 26, 2003

Replies: 1

Views: 10K

How Do You Calculate Curvature and Osculating Circles for a Helical Path?

Oct 22, 2003 · Replies 5 · Oct 24, 2003

Replies: 5

Views: 6K

What Is the Meaning of Permutations in Mathematics?

Oct 16, 2003 · Replies 2 · Oct 24, 2003

Replies: 2

Views: 6K

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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