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.

Threads

Graduate Can a subgroup be mapped onto its parent group as a homomorphism?

  • majutsu
  • · Replies 3 ·
Replies
3

Graduate Some clarification on upper triangular matrices please.

  • gravenewworld
  • · Replies 2 ·
Replies
2

Undergrad Finding Commuting Permutations in S_6 for alpha=(1 2 4 5)

  • SqrachMasda
  • · Replies 11 ·
Replies
11

Graduate Hilbert space and infinite norm vectors

  • seratend
  • · Replies 4 ·
Replies
4

Undergrad How Do You Solve 4x=7 (mod 45) Using Remodularization Concepts?

  • oliver$
  • · Replies 3 ·
Replies
3

Graduate Finding Elements of a Quotient Ring

  • Soccer4822
  • · Replies 2 ·
Replies
2

Graduate Can Someone explain Dedikind cuts?

  • majutsu
  • · Replies 11 ·
Replies
11

Graduate Solving Vector Spaces Problems with Calculus

  • moham_87
  • · Replies 3 ·
Replies
3

Graduate A Short Course on Quantum Matrices: Understanding Notation Basics

  • ^_^
  • · Replies 2 ·
Replies
2

High School Why Does (1/3)*3 = 1 and Not .9 Repeating?

  • ldzcableguy
  • · Replies 53 ·
2
Replies
53

Undergrad Understanding the Pseudoinverse: What is it and How Does it Work?

  • Cyrus
  • · Replies 4 ·
Replies
4

Undergrad How Many Left Cosets of <a^4> in <a> Are There?

  • semidevil
  • · Replies 4 ·
Replies
4

Undergrad How do I show that A is not diagonalizable?

  • quasar987
  • · Replies 3 ·
Replies
3

Undergrad Is my linear algebra book's definition of Euclidean space correct?

  • quasar987
  • · Replies 6 ·
Replies
6

High School How to Prove Zero Product Property for Rational Numbers?

  • MathematicalMatt
  • · Replies 3 ·
Replies
3

Graduate Orthogonal projection, orthonormal basis, coordinate vector of the polynomial?

  • belleamie
  • · Replies 2 ·
Replies
2

Graduate LUB and Nested Interval Equivalancy

  • dogma
  • · Replies 5 ·
Replies
5

Graduate How Rademacher Derived His Formula for Partitioning Integers

  • Janitor
  • · Replies 4 ·
Replies
4

Undergrad Modulo arithmetic (?) question

  • devious_
  • · Replies 10 ·
Replies
10

Graduate Surjective and bijective mapping

  • Bernoulli
  • · Replies 5 ·
Replies
5

Undergrad Proof of ab=0 <--> (a=0 or b=0) without Division

  • Bartholomew
  • · Replies 17 ·
Replies
17

High School Efficient Methods for 3x3 Matrix Multiplication

  • CollectiveRocker
  • · Replies 2 ·
Replies
2
Replies
4

Undergrad Finding the eigenvalue for a given graph

  • Falnom
  • · Replies 2 ·
Replies
2

Graduate Vectors Property: Necessary & Sufficient Conditions

  • tc
  • · Replies 2 ·
Replies
2

Graduate How Can You Prove the Axioms of Norms and Use Them to Test Convergence?

  • juniorgirl06
  • · Replies 5 ·
Replies
5

Graduate Prove A' is the Generalized Inverse of A When A'A is Idempotent

  • siucw
  • · Replies 11 ·
Replies
11

Undergrad Permutations and Transpositions problem help

  • jeannie165
  • · Replies 11 ·
Replies
11

Graduate Verifying F_5[x]/(x^4+1) is a Field

  • T-O7
  • · Replies 12 ·
Replies
12

Graduate What is the concept of injection and surjection?

  • SqrachMasda
  • · Replies 5 ·
Replies
5

Graduate Total potential energy in matrix

  • omgitsroy326
  • · Replies 2 ·
Replies
2

Undergrad Find Linear Combinations for {1, x, x^2, x^3}

  • FrostScYthe
  • · Replies 2 ·
Replies
2

Undergrad Cyclic Group U(14): Generating Elements with <3> to Show Cyclic Property

  • semidevil
  • · Replies 3 ·
Replies
3

Graduate Is x^4 - 14x^2 + 9 = 0 irreducible in Q?

  • Machinus
  • · Replies 2 ·
Replies
2

Undergrad What is the connection between Diophantine equations and number theory?

  • drdolittle
  • · Replies 2 ·
Replies
2

Undergrad Help whit a problem. (I have no idea)

  • mprm86
  • · Replies 3 ·
Replies
3

Graduate What are the key properties of functors and how are they used in mathematics?

  • jcsd
  • · Replies 4 ·
Replies
4

Graduate Lie group (additional condition)

  • namlessom
  • · Replies 2 ·
Replies
2

Graduate I need a proof for this binomial property.

  • T.Rex
  • · Replies 6 ·
Replies
6

Graduate Why are groups, rings, and fields defined in the way that they are?

  • gravenewworld
  • · Replies 3 ·
Replies
3

Graduate Is H Always a Normal Subgroup in a Group of Even Order?

  • cmurphy
  • · Replies 2 ·
Replies
2

Undergrad How Can I Find All Homomorphisms from Z to Z mod 12?

  • cmurphy
  • · Replies 2 ·
Replies
2

Undergrad Theorema of Bezout: Finding f & e with Examples

  • marlon
  • · Replies 5 ·
Replies
5

Graduate Can De Branges' Theorem Make Factoring Prime Numbers Easier for RSA Encryption?

  • ramollari
  • · Replies 6 ·
Replies
6

High School Multiplication (powers) of fractions

  • bimochan
  • · Replies 19 ·
Replies
19

Graduate Does Every Linear Operator Have a Nontrivial Invariant Subspace?

  • gravenewworld
  • · Replies 6 ·
Replies
6

Graduate Proving F is Finite: A Perspective on Ring Homomorphisms

  • dogma
  • · Replies 3 ·
Replies
3

Graduate A bit of trouble with Galois groups

  • Euclid
  • · Replies 2 ·
Replies
2

Undergrad Finding Cosets with H = {0, 3, 6} under Z(9): Understanding the Starting Values

  • semidevil
  • · Replies 2 ·
Replies
2

Undergrad Solving a System of Equations with Matrix

  • LostInSpace
  • · Replies 2 ·
Replies
2

Undergrad Optimizing Integer Comparison without If Statements

  • gerald
  • · Replies 5 ·
Replies
5

Undergrad Linear Algebra HELP: Closest Vector to v in R^4

  • rayveldkamp
  • · Replies 2 ·
Replies
2

Graduate Is <Z,+> with <Z,+> a valid isomorphism? Why or why not?

  • SqrachMasda
  • · Replies 11 ·
Replies
11

Graduate Solve Matrix Hyperplane: Find A & B | Please Help!

  • Mathguy
  • · Replies 3 ·
Replies
3

Graduate Prove Beta is an isomorphism of groups

  • SqrachMasda
  • · Replies 3 ·
Replies
3

Undergrad Nullspace and Column Space Question

  • Bouchart
  • · Replies 2 ·
Replies
2

Graduate What is the group of automorphisms of S_3?

  • T-O7
  • · Replies 2 ·
Replies
2

Graduate Eigenvalues Problem: Show Inverse of Diagonalizable Matrix A

  • tc
  • · Replies 4 ·
Replies
4

Graduate How Does Euler's Formula Lead to e^(iπ) = -1?

  • kreil
  • · Replies 3 ·
Replies
3

Undergrad Can a non-zero matrix multiply itself to become zero matrix?

  • kakarukeys
  • · Replies 6 ·
Replies
6

Graduate Number of Elements of Order 5 in S7 Permutation Group

  • astronut24
  • · Replies 9 ·
Replies
9

Graduate How Do You Find Automorphism in a Group G?

  • semidevil
  • · Replies 10 ·
Replies
10

Graduate Existence of a Polynomial Divisor for Roots in a Field Extension

  • Jin314159
  • · Replies 2 ·
Replies
2

Graduate Proving Finite Solutions of phi(x)=n for Fixed Integer n

  • b0mb0nika
  • · Replies 2 ·
Replies
2

Undergrad Write the system in equation form?

  • mathrocks
  • · Replies 2 ·
Replies
2

Graduate What Is the Relationship Between m, n, and x in the 3x+1 Problem?

  • FromRussiaWithLove
  • · Replies 2 ·
Replies
2

Undergrad Finding the Basis for Repeated Eigenvalues: Explained

  • mathrocks
  • · Replies 2 ·
Replies
2

Undergrad Is There a Solution to the Equation A=x^b mod p?

  • Chu
  • · Replies 3 ·
Replies
3

Undergrad Prove Pythagorean Triples: 3k, 4k, 5k | Answer Yay/Nay

  • 1+1=1
  • · Replies 7 ·
Replies
7

Undergrad What is the relationship between GCD, LCM, and relatively prime numbers?

  • 1+1=1
  • · Replies 3 ·
Replies
3

Graduate RSA Encryption: Finding Primes to Make Decryption Difficult

  • Zurtex
  • · Replies 3 ·
Replies
3

High School What Is the Alphabetical Rank of Ought and Tough?

  • gauravkukreja
  • · Replies 2 ·
Replies
2

Graduate Why Does [d/[n]^2] * n Find the Closest Point to the Origin on a Plane?

  • bezgin
  • · Replies 2 ·
Replies
2

Undergrad Geometric Descr. of 1-1 Function from Square to Circle

  • theFuture
  • · Replies 2 ·
Replies
2

Graduate Column Spaces and Rank of Matrix Multiplication: Insights and Proof

  • loli12
  • · Replies 2 ·
Replies
2

High School Is a Progression a Series or a Sequence?

  • Cheman
  • · Replies 3 ·
Replies
3

Graduate Group Actions on Sets: Understanding the Permutation Group S_3

  • T-O7
  • · Replies 3 ·
Replies
3

Graduate Are Non-Prime Numbers Affected by Reimann's Critical Line?

  • Canute
  • · Replies 11 ·
Replies
11

Undergrad Solving Equation ABXC = D with Matrix Inverses

  • twoflower
  • · Replies 4 ·
Replies
4

Undergrad How Can a^r = 1 mod N Be Expressed Differently If a and N Are Coprime?

  • Baggio
  • · Replies 2 ·
Replies
2

Undergrad Have You Discovered This Recursive Formula for Sums of Powers?

  • StatusX
  • · Replies 3 ·
Replies
3

Undergrad Why is Perpendicularity in 2D and 3D Important?

  • bezgin
  • · Replies 5 ·
Replies
5

Graduate How to Deduce the Sum of Squares of Divisors from Canonical Representation?

  • 1+1=1
  • · Replies 2 ·
Replies
2

Undergrad Solving AxB = (B-1A-1)-1: Inverse Matrix Proof

  • Cannonstar
  • · Replies 2 ·
Replies
2

Undergrad Number of possible electoral college ties

  • Loren Booda
  • · Replies 11 ·
Replies
11

Undergrad Coordinate transformation matrix?

  • Will_C
  • · Replies 3 ·
Replies
3

Graduate Solve Laplace Expansion Determinant -2a,-2b,-2c,2p+x,2q+y,2r+z,3x,3y,3z

  • matrix_204
  • · Replies 2 ·
Replies
2

Graduate How Does Pi Squared Relate to Integer Pythagorean Triples?

  • arivero
  • · Replies 2 ·
Replies
2

Graduate A primality test for Fermat numbers faster than Pépin's test ?

  • T.Rex
  • · Replies 2 ·
Replies
2

Undergrad Is the Matrix A with Entries aij=min(i,j) Always Invertible?

  • RobandJoanna
  • · Replies 2 ·
Replies
2

Undergrad Vector Operations in Polar Coordinates?

  • Poweranimals
  • · Replies 2 ·
Replies
2

Undergrad Division theoryand Prime Number theory

  • Moses
  • · Replies 3 ·
Replies
3

Graduate Generator redefined more rigorously

  • synergy
  • · Replies 14 ·
Replies
14

Undergrad Finding all solutions of Ax = y

  • finalfreak
  • · Replies 2 ·
Replies
2

Graduate How Can Gram-Schmidt Prove dim(w)=dim(V)-1?

  • theFuture
  • · Replies 2 ·
Replies
2

Graduate How can we show that x^m is in a normal subgroup N of G if |G/N| = m?

  • afirican
  • · Replies 2 ·
Replies
2

High School Prime Factorization of 49 + 39 - MathFest 2004

  • devious_
  • · Replies 2 ·
Replies
2

Undergrad Proving Triangle Midpoint Sum Equals Side Length Sum

  • vg19
  • · Replies 3 ·
Replies
3

Undergrad An Algorithm to find a Prime Decompisition

  • Chu
  • · Replies 2 ·
Replies
2

Graduate What Does This Subspace Expression Mean?

  • jbmap
  • · Replies 10 ·
Replies
10