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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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Order of Group Elements in Abelian and Non-Abelian Groups

Mar 26, 2005 · Replies 7 · Mar 27, 2005

Replies: 7

Views: 3K

Understanding Quadric Surfaces in Computer Vision | Forsyth & Ponce

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 3K

Finding A^3: Multiplication of Matrices

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 2K

Is It Possible to Prove Normality of Polynomials?

Mar 25, 2005 · Replies 5 · Mar 26, 2005

Replies: 5

Views: 3K

Proving G is Abelian: A Group Theory Case

Mar 26, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 2K

Solving the Group Theory Conundrum: Proving 'a' is in Z(G)".

Mar 26, 2005 · Replies 3 · Mar 26, 2005

Replies: 3

Views: 3K

Vector, Sub, Column, and Row Spaces

Mar 24, 2005 · Replies 26 · Mar 25, 2005

Replies: 26

Views: 6K

Plan of attack for showing irreducibility?

Mar 24, 2005 · Replies 6 · Mar 24, 2005

Replies: 6

Views: 3K

Standard Basis Math: Find Point X w/ B-Coord Vector X

Mar 17, 2005 · Replies 2 · Mar 24, 2005

Replies: 2

Views: 3K

Irrational digits countably infinite?

Mar 18, 2005 · Replies 6 · Mar 24, 2005

Replies: 6

Views: 5K

Finding Conjugacy Classes in D5 Group

Mar 3, 2005 · Replies 10 · Mar 23, 2005

Replies: 10

Views: 4K

Is There a Generalization of Fermat's Last Theorem?

Mar 11, 2005 · Replies 11 · Mar 22, 2005

Replies: 11

Views: 4K

What is the closest we have come to

Mar 21, 2005 · Replies 9 · Mar 22, 2005

Replies: 9

Views: 3K

A Simple Explanation of Zeta Function Analytic Continuation and Its Results

Mar 10, 2005 · Replies 5 · Mar 21, 2005

Replies: 5

Views: 3K

Proof Problem: Show f(x-1)=f(x) for All x ∈ E

Mar 20, 2005 · Replies 4 · Mar 21, 2005

Replies: 4

Views: 2K

Infinity: Square of Infinity + 2 Infinity

Feb 12, 2005 · Replies 24 · Mar 21, 2005

Replies: 24

Views: 9K

Is the Rank of Matrix A Equal to the Rank of Matrix M?

Mar 20, 2005 · Replies 4 · Mar 21, 2005

Replies: 4

Views: 2K

Eigenvalues Redux: Deriving the Product of Eigenvalues = Determinant

Mar 18, 2005 · Replies 29 · Mar 20, 2005

Replies: 29

Views: 6K

Does matrix A belong to span(A_1,A_2, )

Mar 17, 2005 · Replies 3 · Mar 18, 2005

Replies: 3

Views: 12K

Approximating Pi and e with Linear Algebra

Mar 16, 2005 · Replies 3 · Mar 18, 2005

Replies: 3

Views: 3K

How to Find the Inverse of a Matrix Modulo 26?

Mar 14, 2005 · Replies 24 · Mar 18, 2005

Replies: 24

Views: 22K

Question about finding last digits of numbers

Mar 10, 2005 · Replies 2 · Mar 18, 2005

Replies: 2

Views: 8K

Is x^6-2x^3-1 Irreducible Over Q?

Mar 16, 2005 · Replies 4 · Mar 17, 2005

Replies: 4

Views: 4K

Proof of composite linear transformations

Mar 9, 2005 · Replies 2 · Mar 16, 2005

Replies: 2

Views: 4K

Understanding Partially Ordered Sets: General and Specific Elements Explained

Mar 11, 2005 · Replies 11 · Mar 16, 2005

Replies: 11

Views: 4K

What Are the Eigenvalues and Characteristic Polynomials of a Special 4x4 Matrix?

Mar 15, 2005 · Replies 7 · Mar 16, 2005

Replies: 7

Views: 6K

Proving Non-Trivial Trees Have At Least 2 Vertices with Degree <2

Mar 2, 2005 · Replies 26 · Mar 15, 2005

Replies: 26

Views: 11K

Calculating Coefficients for Dirichlet Series Expansion of a Function

Mar 8, 2005 · Replies 2 · Mar 15, 2005

Replies: 2

Views: 3K

Need desparate help on this question concerning finding a positive integer

Mar 14, 2005 · Replies 6 · Mar 14, 2005

Replies: 6

Views: 2K

Is there a preferred orientation for the x and y axes in physics?

Mar 13, 2005 · Replies 2 · Mar 14, 2005

Replies: 2

Views: 2K

Solving for Integers a and b in a Divisibility Equation

Mar 13, 2005 · Replies 3 · Mar 13, 2005

Replies: 3

Views: 7K

Questions on Remainder & Integer Divisibility

Mar 13, 2005 · Replies 4 · Mar 13, 2005

Replies: 4

Views: 3K

Pi doesnt have reapting random digits

Oct 14, 2004 · Replies 66 · Mar 13, 2005

3

Replies: 66

Views: 13K

Does 0 Belong to the Center of a Lie Algebra?

Mar 13, 2005 · Replies 2 · Mar 13, 2005

Replies: 2

Views: 4K

Is the Square Root of 2 Irrational?

Mar 5, 2005 · Replies 11 · Mar 12, 2005

Replies: 11

Views: 3K

Help me about loop invariant of LCM

Mar 5, 2005 · Replies 2 · Mar 12, 2005

Replies: 2

Views: 4K

The GIMPS project has found a new Mersenne prime number: M42.

Feb 26, 2005 · Replies 4 · Mar 11, 2005

Replies: 4

Views: 4K

Unraveling Euler's Formula: e^(pi*i) +1 = 0

Mar 11, 2005 · Replies 3 · Mar 11, 2005

Replies: 3

Views: 2K

Hairy billiard balls and eigenvectors

Mar 9, 2005 · Replies 4 · Mar 11, 2005

Replies: 4

Views: 4K

How to Clarify Sylow Subgroup Intersections in a Group of Order 48?

Mar 9, 2005 · Replies 7 · Mar 9, 2005

Replies: 7

Views: 4K

Determine all the ideals of the ring Z

Mar 7, 2005 · Replies 5 · Mar 8, 2005

Replies: 5

Views: 4K

Summation of S(N): Infinite/Finite?

Mar 7, 2005 · Replies 7 · Mar 8, 2005

Replies: 7

Views: 3K

Proving Continuity of F:XxI->I with Continuous Functions

Mar 7, 2005 · Replies 4 · Mar 8, 2005

Replies: 4

Views: 2K

Show 'a' is Irreducible: If R a Max Ideal in R

Mar 7, 2005 · Replies 2 · Mar 8, 2005

Replies: 2

Views: 4K

Generating Set for the Symmetric Group - Question

Mar 7, 2005 · Replies 8 · Mar 8, 2005

Replies: 8

Views: 6K

Absurdity of Cantor's Diagonal Slash

Mar 2, 2005 · Replies 44 · Mar 7, 2005

2

Replies: 44

Views: 13K

Finding the Degree of \sqrt{3} + \sqrt[3]{4} Over Q: A Polynomial Search

Mar 6, 2005 · Replies 6 · Mar 7, 2005

Replies: 6

Views: 8K

Proving Isomorphism between Vector Space and Polynomial Space

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 3K

Understanding Coordinate Vectors for Polynomials in P3

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 2K

Prove/Disprove Euclidean Domains: Unique q & r Exist?

Mar 6, 2005 · Replies 2 · Mar 6, 2005

Replies: 2

Views: 3K

Is There a Proven Method for Finding Prime Numbers?

Mar 3, 2005 · Replies 10 · Mar 6, 2005

Replies: 10

Views: 3K

Diagonalizing a 3x3 second derivative matrix

Mar 1, 2005 · Replies 7 · Mar 5, 2005

Replies: 7

Views: 7K

How Does Euler's Formula e^(2*pi*i) Evaluate to 1?

Jan 25, 2005 · Replies 7 · Mar 5, 2005

Replies: 7

Views: 4K

How Does Fermat's Little Theorem Apply to Calculating 3^302 (mod 5)?

Mar 3, 2005 · Replies 3 · Mar 3, 2005

Replies: 3

Views: 2K

Systems of equations - consistency

Mar 1, 2005 · Replies 5 · Mar 3, 2005

Replies: 5

Views: 10K

Solving A^2 + 3A + I = 0: Inverse & -A-3I

Feb 28, 2005 · Replies 11 · Mar 3, 2005

Replies: 11

Views: 3K

How Can We Determine the Number of Abelian Groups of Order p^n?

Feb 23, 2005 · Replies 2 · Mar 3, 2005

Replies: 2

Views: 2K

A Question on Integrating Expansions of Infinities

Mar 1, 2005 · Replies 2 · Mar 1, 2005

Replies: 2

Views: 3K

Hypercomplex Numbers: Hamilton Postulate & Algebra

Feb 22, 2005 · Replies 2 · Mar 1, 2005

Replies: 2

Views: 3K

A trick to calculate Pi(a) for any a?

Feb 19, 2005 · Replies 9 · Feb 28, 2005

Replies: 9

Views: 3K

Summing Powers of 10: Bernoulli's Method

Feb 27, 2005 · Replies 6 · Feb 28, 2005

Replies: 6

Views: 6K

How is multiplication defined and how does it relate to the natural numbers?

Feb 27, 2005 · Replies 7 · Feb 27, 2005

Replies: 7

Views: 3K

Find Idempotent Element in Z/mnZ (m,n Relatively Prime)

Feb 27, 2005 · Replies 2 · Feb 27, 2005

Replies: 2

Views: 5K

Proving (1+a2)(1+a3)...(1+an)=0 for Any Finite Field F

Feb 26, 2005 · Replies 5 · Feb 27, 2005

Replies: 5

Views: 3K

Group Theory Basics: Order & Cyclic Groups

Feb 19, 2005 · Replies 2 · Feb 26, 2005

Replies: 2

Views: 3K

What is the Integral Representation of Pi(x)?

Feb 23, 2005 · Replies 30 · Feb 26, 2005

2

Replies: 30

Views: 6K

Is There a Solution for x^4 ≡ 2 (mod p) When p ≡ 1 (mod 4)?

Feb 17, 2005 · Replies 2 · Feb 25, 2005

Replies: 2

Views: 4K

Proving Isomorphism of Groups with Elements of Same Order

Feb 23, 2005 · Replies 6 · Feb 24, 2005

Replies: 6

Views: 4K

Can the multiplicative group of a finite field be proven to be cyclic?

Feb 24, 2005 · Replies 2 · Feb 24, 2005

Replies: 2

Views: 2K

Proving 1 p-Sylow Subgroup of G is Normal

Feb 24, 2005 · Replies 2 · Feb 24, 2005

Replies: 2

Views: 3K

Solve a Riddle with Base System Minus 1 - Nadine

Feb 23, 2005 · Replies 3 · Feb 23, 2005

Replies: 3

Views: 9K

Understanding Wiles' Proof of Fermat's Last Theorem: A Beginner's Guide

Feb 10, 2005 · Replies 13 · Feb 23, 2005

Replies: 13

Views: 4K

Vectors & Matrices Defined Up to Scale

Feb 22, 2005 · Replies 2 · Feb 23, 2005

Replies: 2

Views: 4K

Factoring Pattern for ax^2 + bx + c

Feb 19, 2005 · Replies 5 · Feb 22, 2005

Replies: 5

Views: 7K

Solving a Diophantine Equation with $4000 and Cows, Lambs & Piglets

Feb 16, 2005 · Replies 2 · Feb 21, 2005

Replies: 2

Views: 5K

Sharipov's linear algebra textbook

Jan 1, 2005 · Replies 25 · Feb 21, 2005

Replies: 25

Views: 12K

What Are the Real-World Applications of Linear Transformations?

Feb 20, 2005 · Replies 3 · Feb 21, 2005

Replies: 3

Views: 3K

A group theoretic puzzle in solid geometry

Feb 15, 2005 · Replies 7 · Feb 19, 2005

Replies: 7

Views: 3K

What is Rational Canonical Form and How is it Used in Rings and Fields?

Feb 18, 2005 · Replies 4 · Feb 19, 2005

Replies: 4

Views: 7K

Understanding Numbers: Definition, Symbols, and Cardinality Explained

Feb 11, 2005 · Replies 15 · Feb 18, 2005

Replies: 15

Views: 4K

Can x^n-a=0 have n real roots for n>2?

Feb 18, 2005 · Replies 3 · Feb 18, 2005

Replies: 3

Views: 3K

How can A-orthogonal vector sets be determined using positive definite matrices?

Feb 17, 2005 · Replies 4 · Feb 17, 2005

Replies: 4

Views: 11K

Need some help with basic complex variables (no proofs)

Feb 17, 2005 · Replies 9 · Feb 17, 2005

Replies: 9

Views: 3K

Matrix rep. of Linear Transformation

Feb 9, 2005 · Replies 2 · Feb 17, 2005

Replies: 2

Views: 4K

Proving R^2 is a Vector Space: Finding Zero Vector & More

Feb 15, 2005 · Replies 8 · Feb 17, 2005

Replies: 8

Views: 3K

A diophantine puzzle for students

Dec 1, 2004 · Replies 10 · Feb 16, 2005

Replies: 10

Views: 4K

Can any real number be represented by a continued fraction?

Feb 9, 2005 · Replies 24 · Feb 16, 2005

Replies: 24

Views: 5K

Minimal and characteristic polynomial

Feb 15, 2005 · Replies 4 · Feb 16, 2005

Replies: 4

Views: 9K

Headache about Kollatz algorythm

Feb 6, 2005 · Replies 2 · Feb 15, 2005

Replies: 2

Views: 2K

Proofing Catalan Numbers: A Combinatoric Approach

Feb 14, 2005 · Replies 3 · Feb 14, 2005

Replies: 3

Views: 6K

Proving Group Properties of \left< U_n, \cdot \right>

Feb 11, 2005 · Replies 8 · Feb 14, 2005

Replies: 8

Views: 4K

Is the System of Equations Inconsistent Despite a Solved Example?

Feb 13, 2005 · Replies 7 · Feb 14, 2005

Replies: 7

Views: 5K

Is Order of Operations the Same in Vector Spaces as in Junior High School?

Feb 13, 2005 · Replies 2 · Feb 13, 2005

Replies: 2

Views: 3K

Counting Non-Isomorphic Binary Operations on G with p Elements

Feb 12, 2005 · Replies 5 · Feb 13, 2005

Replies: 5

Views: 2K

Theorem about symmetric matrices?

Jan 15, 2005 · Replies 7 · Feb 12, 2005

Replies: 7

Views: 5K

Primes in ring of Gauss integers - help

Jan 16, 2005 · Replies 7 · Feb 12, 2005

Replies: 7

Views: 3K

Is Linear Independence Over Z the Same as Linear Independence Over R?

Feb 6, 2005 · Replies 24 · Feb 12, 2005

Replies: 24

Views: 5K

I have discovered a formula for PI(x)

Feb 9, 2005 · Replies 21 · Feb 12, 2005

Replies: 21

Views: 9K

Proving the Order of Elements in a Finite Group G

Feb 11, 2005 · Replies 5 · Feb 12, 2005

Replies: 5

Views: 3K

Prove that T^2 = T0 IFF R(T) C N(T)

Feb 10, 2005 · Replies 2 · Feb 10, 2005

Replies: 2

Views: 2K

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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