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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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Undergrad Is Wilson's Theorem Really a Proof?

Ed Quanta
Mar 6, 2004 · Replies 22 · May 30, 2004

Replies: 22

Graduate Proving (n^4) + 4 is Composite for All n>1: The Odd n Case

Gokul43201
Apr 19, 2004 · Replies 7 · May 27, 2004

Replies: 7

Undergrad Need Explination (linear Indpendance)

stuckie27
May 24, 2004 · Replies 3 · May 25, 2004

Replies: 3

Graduate Circle composition operator / Jacobson Radical

robphy
May 11, 2004 · Replies 10 · May 24, 2004

Replies: 10

High School Find Equation for Parabola-Help, Please?

dmbeluke
May 12, 2004 · Replies 2 · May 19, 2004

Replies: 2

Graduate Can This Mathematical Permutation Problem Be Generalized for Any 4n Terms?

dapet
May 2, 2004 · Replies 2 · May 17, 2004

Replies: 2

Graduate Solving Complex Matrix Problems: Normality, Diagonality, and Unitary Matrices

broegger
May 17, 2004 · Replies 4 · May 17, 2004

Replies: 4

Undergrad Linear Transformation of s u + r V

angel
May 13, 2004 · Replies 2 · May 17, 2004

Replies: 2

High School Smallest Number Divisible by 2-10: Is it 7560?

franz32
May 11, 2004 · Replies 6 · May 13, 2004

Replies: 6

Graduate Belian group A that is the direct sum of cyclic groups

Nexus[Free-DC]
May 11, 2004 · Replies 2 · May 12, 2004

Replies: 2

Graduate Necessary and sufficient condition

tamser0630
May 9, 2004 · Replies 4 · May 10, 2004

Replies: 4

Undergrad Trouble understanding how to formulate rhis problem

angel
May 9, 2004 · Replies 3 · May 10, 2004

Replies: 3

Graduate Can the Polynomial g(x) Have a Solution Modulo Any Integer n?

qaz
May 6, 2004 · Replies 6 · May 10, 2004

Replies: 6

Undergrad Finding vector perpendicular to plane

Michael2003
May 9, 2004 · Replies 6 · May 9, 2004

Replies: 6

Undergrad Sufficiency of n eqs. for n unkwns.

turin
May 7, 2004 · Replies 4 · May 9, 2004

Replies: 4

Undergrad Proving and Disproving a Mathematical Problem: Adding Numbers in Any Base

marisolm
Apr 28, 2004 · Replies 10 · May 6, 2004

Replies: 10

Graduate Some theorems regarding decimal representations

Ed Quanta
Apr 27, 2004 · Replies 2 · May 4, 2004

Replies: 2

Undergrad Anyone able to help with these vectors geometry and planes questions?

Carlito
Apr 27, 2004 · Replies 2 · May 4, 2004

Replies: 2

Undergrad General Solutions for three-point parabola

Hyperreality
Apr 26, 2004 · Replies 2 · May 3, 2004

Replies: 2

Graduate Can the group of rational numbers be generated by a finite set of elements?

Jupiter
Apr 28, 2004 · Replies 7 · Apr 29, 2004

Replies: 7

Undergrad Some theorem regarding rational numbers

Ed Quanta
Apr 28, 2004 · Replies 6 · Apr 28, 2004

Replies: 6

Graduate What are the ideals in various rings?

nocheesie
Apr 27, 2004 · Replies 6 · Apr 28, 2004

Replies: 6

Undergrad Finding the Line of Intersection for Two Planes

theorist
Apr 27, 2004 · Replies 2 · Apr 27, 2004

Replies: 2

Undergrad Understanding Vector Transformation with <1,-1> Translation - Explained

kvzrock
Apr 22, 2004 · Replies 3 · Apr 26, 2004

Replies: 3

Undergrad Reviewing Algebra for CAT6 Test: 3 Challenging Problems

Imparcticle
Apr 25, 2004 · Replies 3 · Apr 25, 2004

Replies: 3

Undergrad The Bilinear Form Kernel in Mathematics

Imparcticle
Apr 21, 2004 · Replies 21 · Apr 24, 2004

Replies: 21

High School Solving Linear Systems: Verify Your Solution

Ericca
Apr 21, 2004 · Replies 9 · Apr 24, 2004

Replies: 9

Undergrad Relationship between Linear Algebra and Differential equations

discoverer02
Apr 21, 2004 · Replies 3 · Apr 23, 2004

Replies: 3

Undergrad Matrix M Formulation for Xn and Xn+1

n0_3sc
Apr 19, 2004 · Replies 3 · Apr 23, 2004

Replies: 3

Graduate Def.: Continuously Indexed Vector Basis?

mstrachan
Apr 16, 2004 · Replies 6 · Apr 22, 2004

Replies: 6

High School Solve the system. (1) 5x + 2y = 5 (2) 3x - 4y = -23

Ericca
Apr 22, 2004 · Replies 1 · Apr 22, 2004

Replies: 1

Undergrad How to solve an exponential ciphers?

sachiyo
Apr 9, 2004 · Replies 3 · Apr 20, 2004

Replies: 3

Graduate How Do Units Determine Norm Values in Rings?

Jupiter
Apr 13, 2004 · Replies 2 · Apr 20, 2004

Replies: 2

High School How to Solve for Integers Modulo n?

JJKorman1
Apr 9, 2004 · Replies 4 · Apr 20, 2004

Replies: 4

High School Why is 10 the Standard Base Number in Mathematics?

steersman
Mar 30, 2004 · Replies 15 · Apr 20, 2004

Replies: 15

Graduate Understanding Group Orders: A Take Home Problem

Wrench
Apr 17, 2004 · Replies 4 · Apr 19, 2004

Replies: 4

Graduate Unitary: Are Det(A) & AdjointA=I Equivalent?

turin
Apr 12, 2004 · Replies 29 · Apr 18, 2004

Replies: 29

Undergrad Prove any three vectors of R^3 are linear independent

philipc
Apr 17, 2004 · Replies 8 · Apr 18, 2004

Replies: 8

Graduate Is 1 considered a prime number in a UFD?

agro
Apr 17, 2004 · Replies 10 · Apr 18, 2004

Replies: 10

Undergrad Homogeneous Equation (easier question)

n0_3sc
Apr 15, 2004 · Replies 2 · Apr 15, 2004

Replies: 2

Undergrad Equivalance Relations Could some one check my work please?

ptex
Apr 13, 2004 · Replies 7 · Apr 15, 2004

Replies: 7

Undergrad Homogenous Equation: Finding 'X' with Non-Invertible Matrix A | Solution Help

n0_3sc
Apr 14, 2004 · Replies 3 · Apr 15, 2004

Replies: 3

High School Find the area of the original parallelogram

travishillier
Apr 6, 2004 · Replies 2 · Apr 14, 2004

Replies: 2

Undergrad Sums of digits of Perfect Squares

tommy05
Apr 10, 2004 · Replies 25 · Apr 12, 2004

Replies: 25

Graduate How Can You Partition Symmetry Groups Using the Multiplication Table Method?

H-bar None
Apr 8, 2004 · Replies 2 · Apr 12, 2004

Replies: 2

Undergrad Guassian elimination and Inverse Matrix

phantomAI
Feb 24, 2004 · Replies 3 · Apr 11, 2004

Replies: 3

Undergrad Geometric App's of Linear Algebra

philosophking
Apr 8, 2004 · Replies 10 · Apr 10, 2004

Replies: 10

High School What Is the Term for Decomposing Numbers into Additive Combinations?

jopux
Mar 25, 2004 · Replies 2 · Apr 9, 2004

Replies: 2

Undergrad Group Theory Basics: Where Can I Learn More?

climbhi
Apr 23, 2003 · Replies 210 · Apr 8, 2004

8

Replies: 210

High School Finding a Book on Basic Number Theory

MC363A
Mar 31, 2004 · Replies 2 · Apr 7, 2004

Replies: 2

Graduate Solve for n: Positive Integer Sequence with Greatest Divisor and LCM

quddusaliquddus
Mar 30, 2004 · Replies 15 · Apr 6, 2004

Replies: 15

Graduate Conjugacy in A_n: Rules & Resources

Jupiter
Apr 4, 2004 · Replies 9 · Apr 5, 2004

Replies: 9

Graduate What Are the Non-abelian Groups of a Given Order?

Jupiter
Apr 4, 2004 · Replies 4 · Apr 5, 2004

Replies: 4

Undergrad Solving Polynomial: p(x) = x^6 + x^4 + x^2 + 1 | Factorization

expscv
Apr 1, 2004 · Replies 19 · Apr 3, 2004

Replies: 19

Undergrad Why Is a Matrix Not Invertible When Its Determinant Is Zero?

Jin314159
Mar 23, 2004 · Replies 4 · Apr 2, 2004

Replies: 4

Undergrad How Do I Solve a Quadratic Regression for a Helicopter Jump Trajectory?

curiousguy
Apr 2, 2004 · Replies 3 · Apr 2, 2004

Replies: 3

High School Formulas For Linear Functions. Can Anyone Me Understand This Problem?

dmbeluke
Mar 31, 2004 · Replies 3 · Mar 31, 2004

Replies: 3

Undergrad Square matrices, determinants and consistency

Asif
Mar 24, 2004 · Replies 2 · Mar 31, 2004

Replies: 2

Undergrad Prove That If rv = 0 Then Either r=0 or v=0

broegger
Mar 30, 2004 · Replies 5 · Mar 30, 2004

Replies: 5

Graduate Anyone familiar with Peano' (or Grassman) algebra?

enigma
Mar 7, 2004 · Replies 5 · Mar 28, 2004

Replies: 5

Undergrad Proving the Only Solution to p is 3: A Simple Mathematical Proof

MathematicalPhysicist
Mar 25, 2004 · Replies 5 · Mar 25, 2004

Replies: 5

High School Solve the Mystery: What is 9 times 7?

bbg5000
Mar 20, 2004 · Replies 3 · Mar 23, 2004

Replies: 3

Undergrad Solving a 4x4 Matrix Determinant: Factor/Cofactor & Triangular Form

phantomAI
Mar 22, 2004 · Replies 3 · Mar 23, 2004

Replies: 3

Graduate Proof of Normal Subgroup Thm- Alternative Strategies

Jupiter
Mar 18, 2004 · Replies 11 · Mar 21, 2004

Replies: 11

Finding the Largest Known Prime: M^2 is the Answer

modmans2ndcoming
Mar 12, 2004 · Replies 2 · Mar 19, 2004

Replies: 2

Undergrad Calculating Value of Continued Fraction

Hypercase
Mar 19, 2004 · Replies 4 · Mar 19, 2004

Replies: 4

Graduate Why do piecewise smooth function spaces require an infinite basis in PDEs?

Ed Quanta
Mar 11, 2004 · Replies 2 · Mar 18, 2004

Replies: 2

Undergrad What Defines an Equivalence Relation?

Ed Quanta
Feb 29, 2004 · Replies 27 · Mar 17, 2004

Replies: 27

Undergrad Proving t(n) Divisible by 3 Implies n is Divisible by 3

Ed Quanta
Mar 14, 2004 · Replies 6 · Mar 16, 2004

Replies: 6

Graduate Geometric Progression of Prime Numbers

UltraPi1
Feb 1, 2004 · Replies 11 · Mar 15, 2004

Replies: 11

Graduate Is the zeta function a complex mapping onto the infinite sum of 1/j^s terms?

Janitor
Mar 15, 2004 · Replies 2 · Mar 15, 2004

Replies: 2

Undergrad How to Calculate a 3x3 Rotation Matrix around a Given Axis?

yanyin
Mar 14, 2004 · Replies 5 · Mar 15, 2004

Replies: 5

High School Solving the Puzzle: Ann and Mary's Ages

bamboozle
Mar 6, 2004 · Replies 2 · Mar 13, 2004

Replies: 2

High School What is the Largest Integer Factored into Two Primes?

x_endlessrain_x
Mar 7, 2004 · Replies 5 · Mar 12, 2004

Replies: 5

Graduate Singular Matrices: Disadvantages, Practical Use & Mass Quantization

Antonio Lao
Mar 9, 2004 · Replies 12 · Mar 10, 2004

Replies: 12

Undergrad Different coordinate system to sketch (x-2y)=sin(pi(x+y))

yanyin
Feb 25, 2004 · Replies 2 · Mar 9, 2004

Replies: 2

Undergrad Man Cashes Cheque: Solve Assumptions to get Amount

bamboozle
Mar 7, 2004 · Replies 2 · Mar 8, 2004

Replies: 2

High School Understanding x=pmodn: An Integer Modular Arithmetic Primer

Ed Quanta
Mar 5, 2004 · Replies 2 · Mar 6, 2004

Replies: 2

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

Bob3141592
Mar 1, 2004 · Replies 12 · Mar 4, 2004

Replies: 12

Graduate Extended Fermat's last theorem.

suyver
Mar 2, 2004 · Replies 7 · Mar 4, 2004

Replies: 7

Graduate Proof of the formula for the nth derivative of a product

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

Replies: 18

Undergrad How Do I Proceed with Variable Row Reduction?

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

Replies: 2

Graduate A partial solution to the Goldbach Conjecture

MathematicalPhysicist
Mar 1, 2004 · Replies 7 · Mar 2, 2004

Replies: 7

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

The Divine Zephyr
Dec 20, 2003 · Replies 9 · Mar 2, 2004

Replies: 9

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

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

Replies: 8

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

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

Replies: 18

Undergrad How to find the matrix for reflecting a triangle over a line in linear algebra?

Johnny Leong
Feb 25, 2004 · Replies 9 · Feb 29, 2004

Replies: 9

Undergrad Understanding the Cross Product of Vectors: Perpendicular Properties Explained

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

2

Replies: 42

Graduate Discovering a Simple Inequality for Divisor Count in Positive Integers

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

Replies: 2

Undergrad Using the Euclidean Algorithm to Find Values for x and y in Linear Combinations?

Caldus
Feb 24, 2004 · Replies 1 · Feb 24, 2004

Replies: 1

Undergrad Searching for Perfect Squares using the Pythagorean Theorem

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

Replies: 2

Undergrad Understanding Irrational Numbers: Is it Possible to Exact Measure?

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

Replies: 4

High School Solving Simultaneous Equations for Confused Students

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

Replies: 9

Graduate Find a linear differentiation transformation

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

Replies: 5

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

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

Replies: 12

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

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

Replies: 2

High School Coefficient of Friction: What is the Equation?

Sarbear777
Feb 10, 2004 · Replies 2 · Feb 18, 2004

Replies: 2

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

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

Replies: 10

Graduate Has the Prime Number Distribution Puzzle Been Cracked?

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

2

Replies: 33

Undergrad Proving Properties of Exponents Using Induction

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

Replies: 3

sidebar

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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