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 Fibonacci-like series for infinite coprime solutions to 5a² + 5ab + b² = 11⁸

  • ramsey2879
  • · Replies 25 ·
Replies
25

Undergrad Solving Triples with xy=a(x+y) and b = xy+xz+yz

  • Yann
  • · Replies 1 ·
Replies
1

Undergrad Algorithm for solving system of nonlinear equations

  • mooshasta
  • · Replies 1 ·
Replies
1

David C. Lay's textbook, need info

  • karakoos23
  • · Replies 4 ·
Replies
4

Graduate Coding in Quaternions and Matrices

  • leon1127
  • · Replies 1 ·
Replies
1

Graduate Sequence of circumscribed Cartesian coordinates

  • Loren Booda
  • · Replies 3 ·
Replies
3

Graduate Proof of existence of a Jordan form?

  • tim_lou
  • · Replies 1 ·
Replies
1

Graduate How to Derive the Exact Expression for Dirichlet Series g(s)?

  • mitchell2007
  • · Replies 5 ·
Replies
5

Graduate What is N-Reciprocity and its significance in number theory?

  • mitchell2007
  • · Replies 1 ·
Replies
1

Graduate How was Fermat's Last Theorem Proved?

  • Victor Sorokine
  • · Replies 15 ·
Replies
15

Undergrad Favourite field of mathematics

  • regularngon
  • · Replies 34 ·
2
Replies
34

Graduate Do all polynomials of degree 1, 2 and 4 have roots in Z_2[x]/(x^4+x+1)?

  • whodoo
  • · Replies 3 ·
Replies
3

Graduate Differences between an axial vector, a pseudo vector and a bivector?

  • Swapnil
  • · Replies 3 ·
Replies
3

Graduate What Are Colimits in Topological Spaces?

  • galoiauss
  • · Replies 14 ·
Replies
14

Graduate Group of translations by a fixed distance

  • Mentz114
  • · Replies 2 ·
Replies
2

Graduate Proving o(G) Divisible by p in Abelian Groups

  • Singularity
  • · Replies 4 ·
Replies
4

Graduate Extending maps defined on dense sets

  • StatusX
  • · Replies 2 ·
Replies
2

Undergrad Standard representation of a vector space

  • quasar_4
  • · Replies 1 ·
Replies
1

Undergrad Algabreic Manipulation of Sigma Notation

  • r16
  • · Replies 6 ·
Replies
6

Graduate Factoring operator and fundamental theorem of algebra

  • tim_lou
  • · Replies 4 ·
Replies
4

Graduate Fundamental groups and homotopy type

  • quasar987
  • · Replies 2 ·
Replies
2

Graduate Is A = I - X(X'X)⁻¹X' idempotent?

  • BigDave48
  • · Replies 4 ·
Replies
4

Graduate Consider the following group in presentation form

  • quasar987
  • · Replies 2 ·
Replies
2

Graduate Thank you!Is my understanding of T-invariant subspaces correct?

  • quasar_4
  • · Replies 3 ·
Replies
3

Undergrad Find n such that x³ + (x+2)ⁿ + (2-x)ⁿ = 0

  • RauLiTo
  • · Replies 1 ·
Replies
1

Graduate Understanding Fibrations and Cofibrations in Model Categories

  • sparkster
  • · Replies 12 ·
Replies
12

Graduate Is a Monoid the Same as a Semi-group in Topology?

  • quasar987
  • · Replies 4 ·
Replies
4

Undergrad Linear independence and dependence

  • yoyo
  • · Replies 3 ·
Replies
3

Undergrad Understanding Span, Basis, and Dimension to Linear Algebra Concepts

  • jlucas134
  • · Replies 3 ·
Replies
3

Graduate Help needed with abstract algebra problems

  • racland
  • · Replies 1 ·
Replies
1

Graduate Show that c and d exist such that ac=b and da=b

  • patelnjigar
  • · Replies 7 ·
Replies
7

Graduate Measuring Gradient Strength in Binary String Mixtures

  • acho
  • · Replies 4 ·
Replies
4

Graduate Proof Even Order Groups Have Element of Order 2

  • clkt
  • · Replies 5 ·
Replies
5

Graduate What Defines a Normal Subgroup in Group Theory?

  • quasar987
  • · Replies 5 ·
Replies
5

Graduate How do Hypercomplex Numbers and Quaternions Work in Supersymmetry?

  • dimsun
  • · Replies 9 ·
Replies
9

Graduate Constructing the Galois Group of f

  • Ant farm
  • · Replies 4 ·
Replies
4

Graduate Dr Euler and characteristic equations

  • Bob3141592
  • · Replies 1 ·
Replies
1

Undergrad How Can I Find Solutions to Diophantine Equations?

  • murshid_islam
  • · Replies 3 ·
Replies
3

Graduate What Are Alternative Infinite Sets of Coprimes Generated by Simple Functions?

  • kureta
  • · Replies 11 ·
Replies
11

Graduate Most rapidly convergent reciprocal prime series equal to 1

  • Loren Booda
  • · Replies 8 ·
Replies
8

Graduate Two questions on linear transformations.

  • MathematicalPhysicist
  • · Replies 5 ·
Replies
5

Undergrad How do I decide if a point is within the triangle

  • Asuralm
  • · Replies 1 ·
Replies
1

Graduate Can a rank-10 matrix be written as sum of rank-1 matrices?

  • MathematicalPhysicist
  • · Replies 2 ·
Replies
2

Graduate A vector space and linear independent set.

  • MathematicalPhysicist
  • · Replies 11 ·
Replies
11

Graduate How to Prove This Fibonacci Identity Involving Squares and Products?

  • ramsey2879
  • · Replies 2 ·
Replies
2

Undergrad Could a set of n verctors in Rm span all of Rm when n<m?

  • yooyo
  • · Replies 5 ·
Replies
5

Undergrad Proving Linearity of L:R(4)→R(4)

  • jlucas134
  • · Replies 8 ·
Replies
8

High School A purely terminological question

  • Ruslan_Sharipov
  • · Replies 14 ·
Replies
14

Graduate Nilpotent matrix invertibility and the equation AB-BA=I

  • kumarrukhaiyar
  • · Replies 2 ·
Replies
2

Graduate Does one zero equal its algebraic conjugate?

  • Gott_ist_tot
  • · Replies 2 ·
Replies
2

Undergrad A different approach to prime numbers

  • kureta
  • · Replies 3 ·
Replies
3

Graduate Inverses of Units: Are All Conjugates Always in the Field?

  • gonzo
  • · Replies 1 ·
Replies
1

Graduate How Do Groups Relate to Symmetry in Mathematics?

  • Cincinnatus
  • · Replies 6 ·
Replies
6

Undergrad Matrix Variables: Solving Mx = b with 2-D Vectors

  • EvLer
  • · Replies 2 ·
Replies
2

Graduate Understanding Vector Spaces in Linear Algebra

  • Parthalan
  • · Replies 2 ·
Replies
2

Graduate Question related to Pell's Equation

  • gonzo
  • · Replies 7 ·
Replies
7

Graduate Proving Isomorphism of Complex Number Conjugate: General Algebraic Systems

  • complexPHILOSOPHY
  • · Replies 3 ·
Replies
3

Undergrad Finding the Limit of a Fibonacci Series

  • tehno
  • · Replies 9 ·
Replies
9

Graduate Why the prime/irreducible distinction?

  • StatusX
  • · Replies 12 ·
Replies
12

Undergrad Spanning sets, and linear independence of them

  • quasar_4
  • · Replies 5 ·
Replies
5

Undergrad Finding pairs (m, n) where (n³ + 27)/(mn - 9) is an integer

  • K Sengupta
  • · Replies 1 ·
Replies
1

Undergrad Automorphisms and some maps that are bijective

  • Gott_ist_tot
  • · Replies 2 ·
Replies
2

Graduate What are the components of an isometry in Euclidean space?

  • sat
  • · Replies 2 ·
Replies
2

Undergrad What Does 'Canonical' Mean in Mathematics?

  • precondition
  • · Replies 9 ·
Replies
9

Graduate Is space just another name for a set?

  • Swapnil
  • · Replies 3 ·
Replies
3

Graduate How can I prove that W contains all elementary matrices?

  • rudo
  • · Replies 8 ·
Replies
8

Undergrad Prove that nm divides k when gcd(m,n)=1 and both m and n divide k

  • Diophantus
  • · Replies 3 ·
Replies
3

Undergrad Understanding Vector Spaces and Subspaces

  • aeroboyo
  • · Replies 16 ·
Replies
16

Graduate Approximate evaluation of this series (exponential sum)

  • Kevin_spencer2
  • · Replies 7 ·
Replies
7

Graduate Proving B is Involutory if A is Idempotent

  • radou
  • · Replies 2 ·
Replies
2

Undergrad Simplifying Cardano's solution to x³ + 5x/3 - 200/27 = 0

  • murshid_islam
  • · Replies 11 ·
Replies
11

Graduate Does Aut(F) form a field or ring under pointwise operations?

  • Edwin
  • · Replies 8 ·
Replies
8

Undergrad Forward difference Newtons formula

  • muskan
  • · Replies 1 ·
Replies
1

Graduate Nonlinear Characters and Finite Groups: A Case Study

  • Ant farm
  • · Replies 1 ·
Replies
1

Graduate Proof of Roots of Unity: Solving a Missing Step

  • gonzo
  • · Replies 2 ·
Replies
2

Graduate Characters of Normal Subgroup of Index 2

  • Ant farm
  • · Replies 3 ·
Replies
3

Graduate Characteristic Polynomial for A with a=-1

  • keddelove
  • · Replies 3 ·
Replies
3

Graduate Inner product of x^p and x^q with weight x^2

  • keddelove
  • · Replies 3 ·
Replies
3

Graduate Is Fermat's Last Theorem Still Unsolvable in Base n?

  • Victor Sorokine
  • · Replies 1 ·
Replies
1

Graduate Wythoff' array and Wechsler's Sequence

  • ramsey2879
  • · Replies 2 ·
Replies
2

High School Why is a sphere considered 2-dimensional if we need 3 dimensions to draw it?

  • Swapnil
  • · Replies 17 ·
Replies
17

Graduate How Can a New Basis Change the Matrix Representation of a Linear Transformation?

  • P3X-018
  • · Replies 1 ·
Replies
1

Graduate Is Hom(Lambda^k(V),Lambda^(k+1)(V)) and element of End(Lambda(V))?

  • precondition
  • · Replies 7 ·
Replies
7

Graduate Showing that αg₁ is in a subgroup of a free abelian group

  • gonzo
  • · Replies 4 ·
Replies
4

Graduate Stationarity Theory: Math Overview

  • navneet1990
  • · Replies 1 ·
Replies
1

Graduate What is a representation of a group?

  • robousy
  • · Replies 25 ·
Replies
25

Undergrad Using Cramer's rule to solve linear equations with complex coefficients?

  • Noone1982
  • · Replies 3 ·
Replies
3

Graduate Vector spaces over fields other than R or C?

  • Nancarrow
  • · Replies 4 ·
Replies
4

Graduate Difference between algebra and module?

  • precondition
  • · Replies 6 ·
Replies
6

Undergrad Solving simultaneous trigonometric equations

  • physicophile
  • · Replies 6 ·
Replies
6

Undergrad What is the connection between complex numbers and vectors in R2?

  • Ratzinger
  • · Replies 6 ·
Replies
6

Graduate Are quaternions simultaneously an algebra, normed vector space, and field?

  • precondition
  • · Replies 2 ·
Replies
2

Graduate Proving the Equality of Rank for Finitely Generated Ideals in Number Fields

  • gonzo
  • · Replies 21 ·
Replies
21

Undergrad One more elementary question, on square roots

  • xalvyn
  • · Replies 3 ·
Replies
3

Graduate Clifford algebra isomorphic to tensor algebra or exterior algebra?

  • precondition
  • · Replies 2 ·
Replies
2

Graduate Lucas-Lehmer Test With Polynomials

  • Milkman
  • · Replies 2 ·
Replies
2

Graduate What is a Graded Algebra with Z_2 Grading?

  • precondition
  • · Replies 5 ·
Replies
5

High School Is There a Square of a Rational Number Between Any Two Positive Rationals?

  • xalvyn
  • · Replies 5 ·
Replies
5

Graduate Writing determinant expansion as a summation

  • lo2
  • · Replies 10 ·
Replies
10

Graduate How can primorials be used to generate a sequence of prime numbers?

  • Playdo
  • · Replies 9 ·
Replies
9