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 Got a bizzare question, appreciate any hints

  • Try hard
  • · Replies 3 ·
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3

Graduate How Do Splitting Fields Relate to Each Other?

  • Euclid
  • · Replies 5 ·
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5

Graduate Proving Invertibility of Matrices: A Small Difference Makes a Big Impact

  • Try hard
  • · Replies 2 ·
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2

High School Solving a 4x4 Determinant for Math Projects

  • jebeagles
  • · Replies 4 ·
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4

Undergrad What is the Basis for the Subspace V in R3 with the Equation x+2y+3z=0?

  • gunnar
  • · Replies 2 ·
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2

Graduate How Do Prime Numbers Divide Factorials?

  • Ethereal
  • · Replies 2 ·
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2

Undergrad How to Solve a Polynomial with Reciprocal Roots?

  • galois427
  • · Replies 2 ·
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2

Graduate How Can You Prove a Spanning Set Theorem Without Summation?

  • loli12
  • · Replies 2 ·
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2

Graduate Showing the Inclusion of Infimum and Supremum in the Closure of a Bounded Set

  • cateater2000
  • · Replies 5 ·
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5

High School Solve 6th Grade Sequence: 1,5,13,25,41,61

  • debrawallenger
  • · Replies 6 ·
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6

Graduate Embarassing question about eigenvectors

  • Ed Quanta
  • · Replies 2 ·
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2

Undergrad Troubleshooting Vector Equations: Proving Collinearity of 3 Concurrent Lines

  • Karate Chop
  • · Replies 1 ·
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1

Undergrad Vector Division: Is It Possible?

  • neutrino
  • · Replies 3 ·
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3

Graduate Question: Elements of Order 2 in Finite Abelian Group

  • Nebula
  • · Replies 10 ·
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10

Undergrad Question about finding the right inverse of a matirx

  • Claire84
  • · Replies 11 ·
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11

Graduate Prove that Q under addition is not isomorphic to R+

  • afirican
  • · Replies 8 ·
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8

Undergrad Efficiency: prime test vs prime generator

  • synergy
  • · Replies 14 ·
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14

Graduate Can a Semigroup with Finitely Many Elements and the Cancellation Law be a Group?

  • T-O7
  • · Replies 5 ·
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5

Undergrad How Can We Determine Convergence of A^n * b in Linear Algebra?

  • gogetagritz
  • · Replies 2 ·
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2

Graduate Can a set of units in a ring form a group under multiplication?

  • dogma
  • · Replies 3 ·
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3

Graduate Clarification of Permuatation Question

  • Redhead711
  • · Replies 2 ·
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2

Graduate Generators of Modular Prime Systems

  • Chu
  • · Replies 2 ·
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2

Graduate Prove property of diophantine equation

  • ascheras
  • · Replies 3 ·
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3

Graduate Is Dirac Notation Appropriate for Proving Hermitian Conjugates of Operators?

  • natski
  • · Replies 2 ·
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2

Graduate Is an Odd Order Permutation Always an Even Permutation?

  • Redhead711
  • · Replies 3 ·
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3

Undergrad Projection of the vector (2,2,1) on the plane

  • gunnar
  • · Replies 9 ·
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9

Graduate Solve Recursion Equation: (n-1)*a[n+1] - n*a[n] + 10*n = 0

  • galois427
  • · Replies 2 ·
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2

Undergrad An interesting matrix identity problem

  • vsage
  • · Replies 8 ·
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8

Graduate Why Do Commuting Invertible Matrices Have a Unique Form?

  • T-O7
  • · Replies 7 ·
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7

Graduate Embarassing question about eigenvectors

  • Ed Quanta
  • · Replies 2 ·
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2

Undergrad Can Ax=0 Be Inconsistent? Solving Linear Equations with a Zero Constant

  • Tryingtolearn
  • · Replies 2 ·
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2

Undergrad Checking Solution for c1, c2, and c3=0

  • gunnar
  • · Replies 6 ·
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6

Undergrad Are Even and Odd Functions Orthogonal?

  • theFuture
  • · Replies 2 ·
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2

Undergrad Finding the Intersection Point of Two Lines in Vector Form

  • ross
  • · Replies 2 ·
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2

Undergrad Solving a Matrix Problem: Help Appreciated!

  • JasonRox
  • · Replies 7 ·
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7

Undergrad Finding primes given a condition

  • galois427
  • · Replies 2 ·
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2

High School Explain vectors from begining to end

  • ConfederateRaider
  • · Replies 7 ·
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7

Undergrad Finding the Inverse of Cubic Functions

  • devious_
  • · Replies 2 ·
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2

Graduate Why do orthogonal matrices have a specific number of independent parameters?

  • Ed Quanta
  • · Replies 3 ·
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3

Undergrad What Are Multi-Dimensional Vectors?

  • bezgin
  • · Replies 13 ·
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13

High School Vector valued and scalar valued functions

  • Odyssey
  • · Replies 2 ·
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2

Undergrad Understanding Matrix Powers: Explained for Linear Algebra Students

  • xenogizmo
  • · Replies 2 ·
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2

Undergrad Understanding the Cosine Formula for Vector Multiplication in 3D Space

  • bezgin
  • · Replies 5 ·
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5

High School Tension Vectors - Grade 12 Algeo

  • lalota
  • · Replies 8 ·
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8

High School Linear Equation: Definition & Meaning

  • Maxwell
  • · Replies 3 ·
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3

Graduate Trouble w/ Lemma: Nullity U Ignored in Finite Vector Space

  • genxhis
  • · Replies 3 ·
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3

Graduate What is the Composition Calculation Method for External Direct Products?

  • williamaholm
  • · Replies 3 ·
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3

Undergrad How Do Permutations Like (a, b)(b, c) Result in (a, b, c)?

  • cmurphy
  • · Replies 2 ·
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2

Graduate Understanding Permutations: Transpositions, Compositions, and Order Explained

  • cmurphy
  • · Replies 2 ·
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2

Graduate Is SL(2,Z3) the Only Group with 24 Elements?

  • ossito_the-diracian
  • · Replies 2 ·
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2

Graduate How many elements of order 5 are in S7?

  • williamaholm
  • · Replies 2 ·
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2

Undergrad What are the range of values of k for the equation (k+1)x^2+4kx+9=0?

  • Gughanath
  • · Replies 34 ·
2
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34

Undergrad What is the proof for triangle ABC with known sides and angle relationships?

  • Blissfulpain
  • · Replies 5 ·
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5

Undergrad What Are Vector Subspaces in Linear Algebra?

  • phy
  • · Replies 2 ·
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2

Undergrad How Does Number Theory Apply to Cryptography?

  • poolwin2001
  • · Replies 3 ·
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3

Undergrad Congruences, Fermats Little Theorm

  • Nebula
  • · Replies 2 ·
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2

Graduate Is Every Group with Self-Inverse Elements Abelian?

  • hedlund
  • · Replies 6 ·
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6

Graduate Arithmetic-geometric mean inequality

  • Ed Quanta
  • · Replies 4 ·
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4

Graduate Proving Induction Problem: P(x) is an Integer for all Natural Numbers n

  • Yoss
  • · Replies 7 ·
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7

Undergrad What is the equation for a vector in R^n that satisfies a given condition?

  • AronH
  • · Replies 4 ·
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4

Undergrad Can Ulam's Spiral Theory Be Enhanced with a Double Spiral Approach?

  • qwantum_phlux
  • · Replies 2 ·
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2

Graduate Is There a Hidden Pattern in Exponentiation Operations on Three Natural Numbers?

  • StatusX
  • · Replies 8 ·
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8

Graduate Prove Polarization Formula in Complex Vector Space

  • HernanV
  • · Replies 2 ·
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2

Graduate Is There a Mistake in Theorem 4.28 on Page 177 of Byron & Fuller's Book?

  • galarant
  • · Replies 2 ·
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2

Undergrad Prove Linear Independence of {u_1,u_2,...,u_k} for k=2,3,...,n-1

  • Phymath
  • · Replies 7 ·
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7

Graduate Showing Two Groups are Isomorphic

  • Oxymoron
  • · Replies 32 ·
2
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32

Graduate What Makes the Negative of a Dedekind Cut Not a Dedekind Cut?

  • cateater2000
  • · Replies 8 ·
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8

Undergrad Interesting problem with possible solution

  • StatusX
  • · Replies 7 ·
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7

Undergrad Basis for the intersection of two spans

  • Try hard
  • · Replies 2 ·
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2

Undergrad Finding a Formula for Sum of Series: 1^2 - 3^2 + 5^2 - 7^2 +...

  • Parth Dave
  • · Replies 19 ·
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19

Undergrad What is the GCD of (a + b, a - b)?

  • cmurphy
  • · Replies 15 ·
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15

Undergrad How Much Force Does a Rope Exert on a Car in This Scenario?

  • Windwaker2004
  • · Replies 2 ·
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2

Graduate How Can a Polynomial's Relationship With Its Derivative Indicate Multiple Roots?

  • IrrationalMind
  • · Replies 9 ·
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9

Undergrad Linear Supply Equation for a Commodity: Solving for Unknown Variables

  • wmosley
  • · Replies 2 ·
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2

Undergrad Proof: x^n + 1 is Valid for Odd n".

  • ascheras
  • · Replies 6 ·
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6

Graduate Frustrating step in a proof - basic abstract algebra

  • Chu
  • · Replies 2 ·
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2

Undergrad Prime Numbers in Set S: Is 2*p>n?

  • atsw
  • · Replies 4 ·
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4

Graduate Computing Distances: Evaluating Sums in Polynomials

  • drago
  • · Replies 3 ·
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3

Undergrad Proving Subspace of Continuous Functions with Integral = 0

  • theFuture
  • · Replies 2 ·
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2

High School Is -1 Considered a Prime Number in Mathematical Discussions?

  • Sven Tingblad
  • · Replies 13 ·
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13

Undergrad Is the Prime Numbers Function f(n) = 3^(n)+2 Always Prime?

  • Anzas
  • · Replies 11 ·
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11

High School Three-Way Arrays: Algebra Basics Explained

  • jcsd
  • · Replies 12 ·
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12

Undergrad What is the Equation for a Series of Numbers with a Repeating Pattern?

  • Logic
  • · Replies 2 ·
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2

Graduate Trouble w/ Maximal Principle (Zorn's Lemma)

  • genxhis
  • · Replies 9 ·
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9

Undergrad What is e? Understanding the Eularian Constant and Its Applications

  • shoryuken
  • · Replies 21 ·
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21

Graduate More algebraic geometry questions

  • Hurkyl
  • · Replies 43 ·
2
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43

High School Solving for Recurring Numbers: Techniques and Applications

  • FateMaster
  • · Replies 6 ·
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6

Graduate What is the Spectrum of the Ring of Continuous Functions Over Rn?

  • Hurkyl
  • · Replies 38 ·
2
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38

Graduate Solving for Generators in Abelian Groups with Multiple Relations

  • Nexus[Free-DC]
  • · Replies 3 ·
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3

Graduate Symmetries of a Regular Quindecagon: Order & Classification

  • Try hard
  • · Replies 2 ·
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2

Undergrad Understanding Upper Triangular, Lower, and Diagonal Matrices

  • JasonRox
  • · Replies 3 ·
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3

High School The Origin & History of Ring & Field: Who Invented Them?

  • gvk
  • · Replies 3 ·
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3

Graduate Is there a misprint in this group theory exercise?

  • pdelong
  • · Replies 22 ·
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22

Undergrad Calculating the Second Norm of a Matrix: Formula and Explanation

  • niko2000
  • · Replies 2 ·
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2

Undergrad Proving the Span of u_1, u_2, ..., u_k and Av

  • Phymath
  • · Replies 3 ·
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3

Graduate Proving Spanning Sets in Vector Spaces

  • Oxymoron
  • · Replies 15 ·
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15

Undergrad How Can We Automate Matrix Inversion for Matrices Near the Identity?

  • radagast
  • · Replies 8 ·
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8

Graduate Cosets are either equal or disjoint

  • Muzza
  • · Replies 12 ·
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12

Undergrad Euler Circuits and Vertices of Even Degree: Proof and Counter-Proof

  • MathNerd
  • · Replies 2 ·
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2

Undergrad Is |a| a Factor of |p0| in a General Polynomial of Degree n?

  • josephcollins
  • · Replies 5 ·
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5