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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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Graduate 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

Graduate Algebraic closure of finite field

Feb 5, 2004 · Replies 9 · Feb 6, 2004

Replies: 9

Views: 9K

Undergrad 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

High School Is zero considered a number in mathematics?

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

2

Replies: 33

Views: 7K

High School 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

Graduate Goldbach Conjecture: Proving the Theory

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

Replies: 20

Views: 9K

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

Feb 3, 2004 · Replies 4 · Feb 4, 2004

Replies: 4

Views: 6K

Undergrad Making Vector Addition programmeable

Feb 3, 2004 · Replies 1 · Feb 3, 2004

Replies: 1

Views: 2K

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

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

Replies: 3

Views: 4K

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

Feb 2, 2004 · Replies 7 · Feb 3, 2004

Replies: 7

Views: 6K

High School Is 1 a Prime Number? - Fact Check

Feb 1, 2004 · Replies 3 · Feb 2, 2004

Replies: 3

Views: 4K

Graduate 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

Undergrad How can a linear transformation be divided and separated into parts?

Jan 25, 2004 · Replies 5 · Jan 31, 2004

Replies: 5

Views: 3K

Graduate 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

Graduate 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

High School What Makes the Number 9 So Mysterious and Fascinating?

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

Replies: 13

Views: 6K

Graduate Ring Theory: Equivalence Relations

Jan 25, 2004 · Replies 10 · Jan 27, 2004

Replies: 10

Views: 4K

Graduate How Do Dynamics and Algebra Interact in the Study of Affine Varieties?

Jan 26, 2004 · Replies 5 · Jan 26, 2004

Replies: 5

Views: 2K

High School Another proof I have a question about

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

Replies: 4

Views: 3K

Undergrad Proving the Distributive Law for Integers

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

Replies: 9

Views: 6K

Graduate Can You Plot the Parametrization for 3D Geometric Algebra?

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

Replies: 2

Views: 6K

High School Simple proof, just using the axioms

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

Replies: 2

Views: 4K

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

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

2

Replies: 37

Views: 10K

Undergrad Semi-Direct Product: Explained in Plain English

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

Replies: 14

Views: 14K

Undergrad What happens as we approach infinity on the number line?

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

Replies: 2

Views: 4K

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

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

Replies: 2

Views: 7K

Graduate 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

Graduate Klein and Cyclic Groups: Definitions and Subgroups

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

Replies: 9

Views: 5K

Graduate How can the parallelogram law be proven?

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

Replies: 3

Views: 10K

High School Decimal fractions and the numer 1

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

Replies: 9

Views: 4K

Undergrad Draw Equipotential Lines & Understand Electrical Fields

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

Replies: 4

Views: 4K

Graduate Has the Poincare Conjecture Finally Been Solved?

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

Replies: 4

Views: 6K

Graduate What Are Perfect Numbers and Why Are They So Mysterious?

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

Replies: 18

Views: 10K

Graduate 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

Graduate Can't solve a problem about subspaces

Jan 3, 2004 · Replies 6 · Jan 8, 2004

Replies: 6

Views: 4K

Undergrad Showing 2 Lines Lie in Same Plane: Equation Solution

Jan 3, 2004 · Replies 5 · Jan 7, 2004

Replies: 5

Views: 14K

Graduate Fourier analysis of the prime distribution

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

Replies: 2

Views: 6K

High School Find the first five terms of sequence

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

Replies: 4

Views: 3K

Undergrad Matrix Solutions and Gaussian Reduction: An Introduction to Linear Algebra

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

Replies: 4

Views: 13K

Undergrad Finding the Transformation Matrix for Linear Transformations in R^3

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

Replies: 6

Views: 5K

Undergrad Is Computational Number Theory Underrepresented in Online Resources?

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

Replies: 2

Views: 4K

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

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

Replies: 2

Views: 3K

Graduate What is the number of elements in the set {x^(13n) : n is a positive integer}?

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

Replies: 3

Views: 11K

Graduate Trying to track down a Partition theorem

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

Replies: 2

Views: 3K

Undergrad Greatest integer divides p^4 -1

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

Replies: 3

Views: 10K

Graduate Taking the logarithm of the euler product

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

Replies: 2

Views: 6K

Undergrad Divisibility Testing for Prime Numbers

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

Replies: 7

Views: 5K

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

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

Replies: 3

Views: 6K

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

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

Replies: 15

Views: 9K

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

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

Replies: 2

Views: 7K

Graduate 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

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

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

Replies: 8

Views: 11K

Graduate Geometric Algebra: Explaining Commutators on Tri-Vectors

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

Replies: 5

Views: 5K

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

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

Replies: 9

Views: 4K

Graduate Show that if A is nonsingular symmetric matrix

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

Replies: 6

Views: 6K

Graduate Can I Name My Prime Series After Myself?

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

Replies: 10

Views: 4K

Undergrad How Can Vector Proofs Simplify Solving Complex Geometry Problems?

Dec 10, 2003 · Replies 1 · Dec 11, 2003

Replies: 1

Views: 6K

Graduate Understanding Gregory's Formula: A Mathematical Challenge

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

Replies: 8

Views: 8K

High School A query that has only got two different prime factors

Dec 2, 2003 · Replies 5 · Dec 9, 2003

Replies: 5

Views: 7K

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

Dec 7, 2003 · Replies 4 · Dec 7, 2003

Replies: 4

Views: 9K

Undergrad How can I better understand the steps of linear algebra?

Dec 6, 2003 · Replies 2 · Dec 6, 2003

Replies: 2

Views: 4K

Graduate Real primes as complex composites

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

Replies: 2

Views: 4K

Undergrad Elementary Row Operations on Matrices

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

Replies: 3

Views: 21K

High School Benediktov Problem: Solve the Daughters' Egg Selling Challenge

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

Replies: 2

Views: 4K

Graduate Solving an Eigenvalue Problem for Large n Matrix

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

Replies: 5

Views: 4K

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

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

Replies: 2

Views: 4K

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

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

Replies: 6

Views: 6K

Undergrad Logic & Algebra: F Intersect G = ?

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

Replies: 5

Views: 3K

Graduate Definiton of a category question

Nov 15, 2003 · Replies 3 · Nov 16, 2003

Replies: 3

Views: 3K

Graduate Group Theory: Find the order of

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

Replies: 15

Views: 8K

Undergrad Matrices and Matrix Calculations of Linear Algebra

Oct 4, 2003 · Replies 6 · Nov 9, 2003

Replies: 6

Views: 12K

Undergrad Find A Permutation of order 6 in S5

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

Replies: 14

Views: 12K

High School Understanding Normalizing, Det/Adj & Linear Algebra

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

Replies: 2

Views: 7K

Graduate Can the Resultant of Cross Products of Vectors with Zero Resultant also be Zero?

Nov 4, 2003 · Replies 2 · Nov 4, 2003

Replies: 2

Views: 2K

Undergrad 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

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

Nov 1, 2003 · Replies 8 · Nov 1, 2003

Replies: 8

Views: 5K

Undergrad What is M? system of linear equations

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

Replies: 2

Views: 3K

Graduate Proving g2 = u in Dihedral Group of Order 8

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

Replies: 4

Views: 13K

Graduate Bohemian Intellectual Mathematics and Occultism

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

Replies: 1

Views: 11K

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

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

Replies: 5

Views: 6K

Undergrad What Is the Meaning of Permutations in Mathematics?

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

Replies: 2

Views: 6K

Undergrad Is Induction or Contradiction Better for Proving 2n+1 < 2^n When n > 3?

Sep 30, 2003 · Replies 6 · Oct 20, 2003

Replies: 6

Views: 5K

Graduate Noncommotative structural numbers

Oct 16, 2003 · Replies 3 · Oct 19, 2003

Replies: 3

Views: 3K

Undergrad Divisibility of c by a and b but not ab .

Oct 1, 2003 · Replies 3 · Oct 17, 2003

Replies: 3

Views: 12K

Graduate Has the Prime Number Distribution Conjecture Been Cracked?

Sep 30, 2003 · Replies 6 · Oct 16, 2003

Replies: 6

Views: 6K

High School How is division defined in mathematics?

Sep 28, 2003 · Replies 6 · Oct 15, 2003

Replies: 6

Views: 9K

Undergrad Is a*b = |ab| a Group Operation?

Sep 11, 2003 · Replies 12 · Oct 9, 2003

Replies: 12

Views: 17K

Undergrad How Do You Construct a Degree 8 Polynomial with Given Complex and Real Roots?

Oct 5, 2003 · Replies 1 · Oct 5, 2003

Replies: 1

Views: 8K

High School Understanding the Euclidean Algorithm: Solving for Relatively Prime Numbers

Sep 25, 2003 · Replies 2 · Oct 3, 2003

Replies: 2

Views: 5K

Graduate What is the relationship between the magenta and cyan areas?

Sep 30, 2003 · Replies 3 · Oct 2, 2003

Replies: 3

Views: 10K

Undergrad Proving Divisibility: A Corrected Proof and Tips for Improvement

Sep 30, 2003 · Replies 2 · Sep 30, 2003

Replies: 2

Views: 5K

Graduate Is 1ln(5)/2πi Equal to 5 in Complex Number Exponentiation?

Sep 23, 2003 · Replies 9 · Sep 24, 2003

Replies: 9

Views: 5K

Graduate Proof of (m+n*)* = m* + n* in Modern Abstract Algebra

Sep 23, 2003 · Replies 2 · Sep 24, 2003

Replies: 2

Views: 4K

Undergrad Guide to Constructing a Proof by Induction for Natural Numbers

Sep 23, 2003 · Replies 7 · Sep 23, 2003

Replies: 7

Views: 6K

Graduate Understanding Fermat's Last Theorem: A General Overview

Sep 18, 2003 · Replies 10 · Sep 22, 2003

Replies: 10

Views: 7K

Graduate Matrix^0: Is O0 Defined if O is Not a Square Matrix?

Sep 11, 2003 · Replies 15 · Sep 12, 2003

Replies: 15

Views: 5K

Undergrad A plane intersecting another plane

Sep 10, 2003 · Replies 6 · Sep 11, 2003

Replies: 6

Views: 9K

Undergrad Can Matrix Analysis Simplify Linear and Non-Linear Systems?

Aug 12, 2003 · Replies 3 · Aug 13, 2003

Replies: 3

Views: 6K

High School Is Gaussian Elimination Only Used for 3x3 Matrices?

Aug 7, 2003 · Replies 4 · Aug 12, 2003

Replies: 4

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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