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

Undergrad 2 Questions, regarding closure

  • rbzima
  • · Replies 7 ·
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7

Graduate Can 2z^n(z^n + x^n + y^n) Ever Be a Perfect Square for Prime n Greater Than 2?

  • ramsey2879
  • · Replies 2 ·
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2

Graduate Conjecture on triangular numbers T(n)

  • ramsey2879
  • · Replies 19 ·
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19

Graduate Group Theory-solution to polynomial equations

  • Himanshu
  • · Replies 5 ·
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5

Undergrad Solving Higher Order Polynomial: ax + x^3 - x^5 = 0

  • Peregrine
  • · Replies 5 ·
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5

Graduate What are the v_j vectors in Cahn's representation of the Lie algebra of SO(3)?

  • jdstokes
  • · Replies 1 ·
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1

Undergrad Can someone explain Euler angles?

  • makc
  • · Replies 3 ·
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3

Undergrad If gcd(a,b)=1, why does gcd(a,bk) = gcd(a,k)?

  • Hells_Kitchen
  • · Replies 2 ·
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2

Graduate Finding Galois group of splitting field with determinant formula

  • Hello Kitty
  • · Replies 4 ·
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4

Undergrad Prove a few theorems about vector spaces using the axioms

  • ataraxia
  • · Replies 1 ·
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1

Graduate Why Use a - b Instead of a + b in Equivalence Classes of Rings?

  • InquilineKea
  • · Replies 3 ·
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3

Undergrad Can a Direct Proof Show That 1-A is its Own Inverse?

  • torquerotates
  • · Replies 3 ·
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3

Graduate What is the value of this finite sum?

  • Pere Callahan
  • · Replies 2 ·
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2

Undergrad Vector spaces + proving of properties

  • JamesGoh
  • · Replies 28 ·
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28

Graduate Lie Groups and Algebras: Proofs and Potential Errors

  • ala
  • · Replies 5 ·
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5

Undergrad Is there a relationship between remainders and positive integers?

  • Gnoj
  • · Replies 2 ·
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2

Graduate One question related to an ideal of Ring R

  • wowolala
  • · Replies 1 ·
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1

Graduate Why is <2>[x] not maximal in Z[x] if <2> is maximal in Z?

  • wowolala
  • · Replies 6 ·
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6

Undergrad Is T(x,y)=(1,y) a linear transformation?

  • sara_87
  • · Replies 16 ·
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16

Undergrad Eigenvalues and -vectors in class

  • nonequilibrium
  • · Replies 2 ·
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2

High School What is meant by collinear, parallel and coplanar vectors?

  • dcl
  • · Replies 4 ·
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4

Graduate What do you call a maximal orthonormal set?

  • quasar987
  • · Replies 3 ·
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3

Undergrad Puzzling Equation: x^y=y^x - Are There Solutions?

  • Ynaught?
  • · Replies 4 ·
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4

Graduate Problem on linear independence and matrices

  • vince89
  • · Replies 17 ·
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17

Graduate Is Cubing a Permutation in Zp for Primes Equivalent to 2 Mod 3?

  • Hello Kitty
  • · Replies 5 ·
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5

Graduate Derivation of Euler's formula for phi(m)

  • Eus
  • · Replies 4 ·
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4

Undergrad Finding k where 2^k=n in ℤ/p

  • CRGreathouse
  • · Replies 2 ·
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2

Graduate What Are the Properties of G(n) in Group Theory?

  • smoothman
  • · Replies 3 ·
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3

Graduate Proving feasibility of convex linear combination in LP problem

  • dopey9
  • · Replies 2 ·
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2

Graduate Is There a Faster Way to Find Conjugacy Classes in Group Theory?

  • catcherintherye
  • · Replies 1 ·
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1

Graduate Order of Groups: Proving ord(\theta(x)) = ord(x)

  • smoothman
  • · Replies 3 ·
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3

Graduate Constructing a finite field with 10^9 to 10^10 elements in Mathematica

  • Granit_niti
  • · Replies 1 ·
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1

Graduate Can Multilinear Maps Be Represented with Matrices?

  • WWGD
  • · Replies 2 ·
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2

Undergrad How to Find Inverse of a Matrix

  • nanoWatt
  • · Replies 4 ·
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4

Undergrad Why use permutations to define determinants for n×n matrices

  • O.J.
  • · Replies 17 ·
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17

Graduate Quaternions or Vectors: Which is the Better Choice for Electromagnetism?

  • Gerenuk
  • · Replies 1 ·
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1

Graduate Does showing G × H is a group mean verifying the four group axioms?

  • smoothman
  • · Replies 13 ·
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13

Undergrad Cutting equal numbers of different length pieces from a known length

  • jeff_fall2k5
  • · Replies 4 ·
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4

Graduate What groups have exactly 4 subgroups?

  • Mystic998
  • · Replies 3 ·
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3

Undergrad Is the A_n Group the Same as the Dihedral Group D_n?

  • Magister
  • · Replies 1 ·
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1

Graduate Can there be a largest prime within the concept of infinity?

  • Icebreaker
  • · Replies 23 ·
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23

Graduate Understanding Fields: How Can They Be Represented and Applied?

  • nanoWatt
  • · Replies 4 ·
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4

Graduate Finding the count and sorted position of pairs and triplets with bounded sum

  • ramsey2879
  • · Replies 2 ·
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2

Undergrad How to Solve the Tough Diophantine Equation?

  • Izzhov
  • · Replies 6 ·
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6

Graduate How Can I Understand the Representation Theory of Lie Algebras?

  • Jim Kata
  • · Replies 1 ·
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1

Undergrad Gradient of trace of ABA'C with respect to A

  • Ghostrider
  • · Replies 2 ·
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2

Undergrad Can Column Operations be Used to Find the Inverse of a Matrix?

  • rock.freak667
  • · Replies 8 ·
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8

Undergrad Solving for A and B from A²−B²=hj(k²) and 2AB=mjk

  • mconn86
  • · Replies 3 ·
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3

Undergrad Solve (2-i)x + (-3+4i)y = -2+3i

  • BlackIP
  • · Replies 1 ·
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1

Undergrad Write OT as linear combination of OX and OY given division ratios

  • Mtl
  • · Replies 2 ·
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2

Graduate Vector Space Algebra of Minkowski Space

  • thermobum
  • · Replies 4 ·
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4

Graduate Eigenspaces, Kernel, and Span: Understanding with Examples | Question Answered

  • smoothman
  • · Replies 6 ·
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6

High School De Moivre's Theorum and Double-Angle Formulas

  • Jessehk
  • · Replies 4 ·
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4

Undergrad Dot product cross product, where did they come from?

  • dionysian
  • · Replies 21 ·
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21

Graduate Why Isn't the Inverse of My Fundamental Matrix Correct?

  • Diferencialdex
  • · Replies 3 ·
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3

Graduate Is Showing the Uniqueness of Highest Weight a Valid Proof of Irreducibility?

  • lion8172
  • · Replies 2 ·
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2

Undergrad Rank of Matrices: Why Equal to Transpose?

  • Fu Lin
  • · Replies 4 ·
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4

Undergrad If n² is divisible by 6, is n divisible by 6?

  • ToastMonger
  • · Replies 10 ·
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10

Graduate How does a free vector space differ from a standard vector space?

  • matheinste
  • · Replies 11 ·
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11

Undergrad How does row reduction relate to a linear map's matrix?

  • WWGD
  • · Replies 2 ·
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2

Undergrad Two vectors in 3D, always form a plane?

  • blackcat
  • · Replies 18 ·
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18

Undergrad Two disjoint subsets of a 15-element subset of {1,...,2048} with equal sum

  • Doom of Doom
  • · Replies 12 ·
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12

Undergrad Prove a² + ab + b² = c² for a triangle with a 120° angle

  • Ynaught?
  • · Replies 3 ·
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3

Graduate Prove a^2 + b^2 = 3(s^2 + t^2) implies both a and b must are divisible by 3

  • Ceres629
  • · Replies 13 ·
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13

Graduate Can Injectivity of a Matrix Guarantee a Left Inverse?

  • y_lindsay
  • · Replies 1 ·
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1

Undergrad Solve matrix equation for four unknowns

  • jubej
  • · Replies 7 ·
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7

Graduate Linear Transformation to Shrinking/Expand along a given direction

  • birulami
  • · Replies 4 ·
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4

Graduate Proving the Continuity of Projections in Vector Spaces

  • jostpuur
  • · Replies 2 ·
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2

Undergrad Finding integer solutions to y² = x³ + n

  • quila
  • · Replies 15 ·
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15

Graduate What is the Inverse of an Element in Free Vector Spaces?

  • matheinste
  • · Replies 6 ·
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6

Graduate Quadratic residues modulo primes and Fermat's Little Theorem

  • grandnexus
  • · Replies 10 ·
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10

Graduate Negative-definite inner products

  • andytoh
  • · Replies 4 ·
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4

Undergrad Do systems of linear equations in five variables represent graphs in higher dimensions?

  • Liger20
  • · Replies 1 ·
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1

Graduate Identifying elements in V(x)W, V,W V.Spaces

  • WWGD
  • · Replies 4 ·
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4

Graduate How Do You Solve Group Ring Isomorphisms in Mathematics?

  • catcherintherye
  • · Replies 4 ·
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4

Undergrad Simpler proof of Cramer's rule

  • rock.freak667
  • · Replies 2 ·
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2

Graduate Given a real nxn symmetric and non-positive definite matrix,. .

  • kholden
  • · Replies 3 ·
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3

Graduate Finding a Subspace W of R^4 for Direct Sum V(+)W

  • student82
  • · Replies 5 ·
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5

Undergrad I'm trying to prove that a linear map is injective

  • catcherintherye
  • · Replies 1 ·
Replies
1

High School Is Every Integer in the Decimal System Divisible by 5?

  • Prathep
  • · Replies 5 ·
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5

Graduate Proofs that the golden ratio is irrational

  • at3rg0
  • · Replies 15 ·
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15

Graduate Is a diagonal matrix similar to a lower triangular matrix with the same diagonal?

  • thebuttonfreak
  • · Replies 1 ·
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1

Undergrad What are the possible values of the determinant of an orthogonal matrix?

  • salman213
  • · Replies 7 ·
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7

Undergrad What Is the Linear Property of Determinants?

  • Winzer
  • · Replies 1 ·
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1

Undergrad Find Dimension of Nullspace A with Basis Calculation

  • ND3G
  • · Replies 5 ·
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5

Undergrad Can abstract math be understood through concrete examples?

  • pivoxa15
  • · Replies 11 ·
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11

Graduate Order of 2x2 matrix group under mult. mod p

  • SiddharthM
  • · Replies 3 ·
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3

Graduate Counterexample so that (ab)^i=a^ib^i for two consecutive integers

  • SiddharthM
  • · Replies 4 ·
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4

Graduate How to remember the second and third isomorphism theorems intuitively

  • lion8172
  • · Replies 2 ·
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2

Undergrad Vector spaces, Spans and Matrix Determinants

  • ND3G
  • · Replies 6 ·
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6

Undergrad Do Equations in More Than Three Variables Represent Graphs in Higher Dimensions?

  • Liger20
  • · Replies 9 ·
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9

Graduate What Do Homomorphisms on Rings Really Mean?

  • chocok
  • · Replies 3 ·
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3

Graduate Counterexample for an alternate definition for a group

  • SiddharthM
  • · Replies 2 ·
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2

Graduate Galois and Klein 4: Isomorphic or Cyclic?

  • morganjp
  • · Replies 1 ·
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1

Undergrad Matrix algebra over finite fields

  • AngelofMusic
  • · Replies 1 ·
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1

Undergrad Least amount of structure for vector space.

  • matheinste
  • · Replies 9 ·
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9

Graduate Adjoint of a linear operator Definition

  • kingwinner
  • · Replies 15 ·
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15

Undergrad Is 19 = x^2 mod p solvable? p=68659

  • quila
  • · Replies 12 ·
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12

Graduate What is the difference between SO(3,1) and SO(1,3)?

  • Coin
  • · Replies 1 ·
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1

Undergrad How to make a matrix B such that AB=BA

  • yooyo
  • · Replies 36 ·
2
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36