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 What Is the Spectrum of a Linear Operator in L2 Spaces?

  • maxandri
  • · Replies 2 ·
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2

Making a Right R-module Into a Left R-Module - Bland, page 26 ....

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Split Exact Sequences .... Bland, Proposition 3.2.7

  • Math Amateur
  • · Replies 12 ·
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12

Module Over a Division Ring - Blyth Theorem 1.1, Part 4

  • Math Amateur
  • · Replies 2 ·
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2

How Does Condition (2) Imply Condition (3) in Bland's Proposition 3.2.7?

  • Math Amateur
  • · Replies 36 ·
2
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36

Undergrad Eigenvalue as a generalization of frequency

  • npit
  • · Replies 4 ·
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4

Undergrad Proving Vector Space of Circles is Not Axiomatic

  • mikeeey
  • · Replies 2 ·
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2

High School Polynomial Space: Can Degree 2 Fit in 1+x^2?

  • mikeeey
  • · Replies 1 ·
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1

Finitely Cogenerated Modules - Bland Definition 4.1.3, Page 105

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Question in linear algebra, derivation of a certain relation

  • antonni
  • · Replies 3 ·
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3

Bland - Rings and their Modules 2011

  • steenis
  • · Replies 5 ·
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5

High School Understanding Choi's Theorem and Notation in Matrix Theory

  • naima
  • · Replies 8 ·
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8

Undergrad What Are the Key Properties of Scalar Product and the Law of Cosines?

  • Devil Moo
  • · Replies 9 ·
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9

Each exact sequence can be arised by short exact sequences

  • mathmari
  • · Replies 2 ·
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2

Exact Sequences and short exact sequences - basic question

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Hodge Dual as Sequence of Grade Reducing Steps

  • MisterX
  • · Replies 2 ·
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2

Undergrad Simplifying 3 simultaneous equation into one equation

  • Budana
  • · Replies 10 ·
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10

Undergrad Congruence vs equality in mod arithmetic

  • jack476
  • · Replies 3 ·
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3

Graduate Rank 3x4 Complex Matrix Constraints

  • swraman
  • · Replies 3 ·
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3

Undergrad Why is A.A = ||A||^2 in Vector Analysis?

  • parshyaa
  • · Replies 7 ·
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7

Graduate Normalization and Scaling with Matrices

  • doublee89
  • · Replies 5 ·
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5

Undergrad Solving equations with singular matrix

  • Zak
  • · Replies 2 ·
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2

Undergrad Vector components, scalars & coordinate independence

  • Frank Castle
  • · Replies 16 ·
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16

Undergrad Relations & Functions: Types, Examples, Homomorphism

  • mikeeey
  • · Replies 4 ·
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4

Undergrad Unraveling Representations of SU2 & SU3 in Particle Physics

  • Josh1079
  • · Replies 5 ·
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5

Undergrad Decomposing Vectors Using Row Reduction: A Practical Approach

  • dman12
  • · Replies 3 ·
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3

Undergrad Vector Cross Product: Understanding the Perpendicular Result

  • parshyaa
  • · Replies 11 ·
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11

Undergrad Tensor product and ultraproduct construction

  • nomadreid
  • · Replies 2 ·
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2

Help with Projective Algebraic Geometry - Cox et al Section 8.1, Exs 5(a) & 5(b)

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Create an Equation for 3 Offspring Rabbits

  • Dusto
  • · Replies 2 ·
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2

Show that $p(x)|f(x)$: Proving the Divisibility

  • mathmari
  • · Replies 12 ·
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12

High School Mistake when explaining associativity of vector addition

  • CynicusRex
  • · Replies 2 ·
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2

Projective Algebraic Geometry - Exercise 4(a) Cox et al - Section 8.1

  • Math Amateur
  • · Replies 2 ·
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2

Insights Groups and Geometry - Comments

  • micromass
  • · Replies 7 ·
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7

Graduate How Did They Derive Equation (49) from Equation (21) Using Matrix Identities?

  • perplexabot
  • · Replies 11 ·
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11

Undergrad Parametric Representation of a Solution Set

  • askor
  • · Replies 1 ·
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1

Projective Algebraic Geometry - the Projective Plane ....

  • Math Amateur
  • · Replies 8 ·
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8

Help with Exercise 3(c) in Cox et al's Projective Algebraic Geometry

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Make a Perfect Dodecahedron: What Angle to Cut Plywood?

  • arydberg
  • · Replies 13 ·
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13

Peter Needs Help on Cox et al - Section 8.1, Exercise 3(a)

  • Math Amateur
  • · Replies 3 ·
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3

High School Is the intersection of two planes a line?

  • member 587159
  • · Replies 9 ·
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9

Undergrad Is Geometric Algebra inconsistent/circular?

  • malawi_glenn
  • · Replies 32 ·
2
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32

Undergrad Question about decomposition of matrices in SL(2,R)

  • mnb96
  • · Replies 9 ·
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9

Graduate Exterior Algebra Dual for Cross Product & Rank 2 Tensor Det

  • MisterX
  • · Replies 2 ·
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2

Finding a set of vectors that span u,v....

  • shamieh
  • · Replies 1 ·
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1

Algebraic element - Minimal polynomial

  • mathmari
  • · Replies 1 ·
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1

Prime Subfield of Field F: Isomorphic to $\mathbb{Q}$

  • evinda
  • · Replies 1 ·
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1

High School Sets and functions that gain more structure with context

  • ProfuselyQuarky
  • · Replies 9 ·
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9

How to find a non-zero vector in the column space of M

  • shamieh
  • · Replies 1 ·
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1
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1

Undergrad Dimension of the group O(n,R) - How to calc?

  • JuanC97
  • · Replies 3 ·
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3

Undergrad Vector Division: An Explainer of Why It's Not Possible

  • Atizaz Ahmed
  • · Replies 5 ·
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5

High School What Are Imaginary Numbers and How Can They Be Understood?

  • Sobhan
  • · Replies 11 ·
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11

Undergrad Why is this Isometry a rotation?

  • Doradus
  • · Replies 5 ·
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5

Find all the matrices in Jordan form

  • mathmari
  • · Replies 19 ·
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19

Wondering if $R$ is a P.I.D.: Free Modules and Ideals

  • mathmari
  • · Replies 6 ·
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6
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3

Is \(F[x]/<p(x)>\) the Root Field of \(x^4+ax^2+b\)?

  • Kiwi1
  • · Replies 1 ·
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1

Undergrad If pair of polynomials have Greatest Common Factor as 1 ....

  • swampwiz
  • · Replies 1 ·
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1

Undergrad Matrix of columns of polynomials coefficients invertibility

  • swampwiz
  • · Replies 2 ·
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2

Undergrad Algebraically Closed Fields

  • Math Amateur
  • · Replies 8 ·
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8

High School Can a Binary Number be Viewed as an Orthogonal Basis?

  • entropy1
  • · Replies 2 ·
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2

How Does Algebraic Closure Extend to Multivariable Polynomials?

  • Math Amateur
  • · Replies 2 ·
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2

Ideals in Q[x, y] .... Cox, Little and O'Shea, Chapter 1 Section 4

  • Math Amateur
  • · Replies 2 ·
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2

Affine Algebraic Sets in A^2 - Dummit and Foote, page 660, Example 3

  • Math Amateur
  • · Replies 2 ·
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2

High School How Do You Compute the Expression E = AB - B^*A^* with Complex Numbers?

  • TheCanadian
  • · Replies 8 ·
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8

Undergrad Eigenvalues and Eigenvectors question

  • Dank2
  • · Replies 16 ·
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16

Show Im(gf)=Im(g) When f is Onto (Wondering)

  • mathmari
  • · Replies 4 ·
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4

Undergrad Affine Algebraic Sets - General Question

  • Math Amateur
  • · Replies 3 ·
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3

Graduate What is the state of the art in solving polynomial equations?

  • jonjacson
  • · Replies 15 ·
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15

Undergrad Proving Isometries: A Step-By-Step Guide

  • Doradus
  • · Replies 3 ·
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3

Graduate Why Is the Discriminant Non-Positive in the Triangle Inequality Proof?

  • LagrangeEuler
  • · Replies 1 ·
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1

Graduate Understanding the Eigenframe: Definition and Importance

  • K41
  • · Replies 6 ·
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6

Undergrad SU(2) and su(2) have different dimensions?

  • pellman
  • · Replies 2 ·
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2

Undergrad Affine Algebraic Sets - Dummit and Foote, page 660, Ex. 3

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad What is the Inverse of the Function f(x) = e^x + e^(-x) + 1?

  • Eishan M
  • · Replies 3 ·
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3

Undergrad Why do some people only define prime elements in integral domains?

  • Math Amateur
  • · Replies 20 ·
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20

Undergrad Proving Identity for Determinant of $A^tA$

  • tommyxu3
  • · Replies 20 ·
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20

Equivalence of Definitions of Algebras in D&F and Cooperstein | Peter

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad K-algebra/associative algebra - equivalence of definitions

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Polynomials in n indeterminates and UFDs

  • Math Amateur
  • · Replies 5 ·
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5

Prime Elements in Non-Integral Domains?

  • Math Amateur
  • · Replies 1 ·
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1

Statements about subrings and quotient

  • mathmari
  • · Replies 3 ·
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3

Polynomials in n indeterminates and UFDs

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Difference between direct sum and direct product

  • Silviu
  • · Replies 1 ·
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1

Undergrad Chladni plate with Neumann conditions

  • Smollett
  • · Replies 2 ·
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2

High School Why is there a solution to this system?

  • ProfuselyQuarky
  • · Replies 15 ·
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15

(x) and (x,y) are prime ideals of Q[x,y]

  • mathmari
  • · Replies 4 ·
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4

Undergrad Tensor Products of Modules - Bland - Remark, Page 65

  • Math Amateur
  • · Replies 4 ·
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4

Tensor Products of Modules - Bland - Remark, Page 65

  • Math Amateur
  • · Replies 1 ·
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1

Tensor Products and the Free Z-module - Bland Propostion 2.2.3 .... ....

  • Math Amateur
  • · Replies 3 ·
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3
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7

Undergrad How Do Properties of Modulus Algebra Apply to RSA and Diffie-Hellman?

  • FrankJ777
  • · Replies 12 ·
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12

These are the only submodule

  • mathmari
  • · Replies 12 ·
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12

Undergrad Multiple time derivatives of gravitational potential

  • Belginator
  • · Replies 2 ·
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2

Undergrad Spherical coordinates via a rotation matrix

  • unicornflyers
  • · Replies 3 ·
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3

Undergrad What kind of space is the space of spinors?

  • davi2686
  • · Replies 4 ·
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4

Undergrad Eigenspectra and Empirical Orthogonal Functions

  • ecastro
  • · Replies 4 ·
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4

Undergrad Directly Finite and Directly Infinite R-Modules - Bland S2.2

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Same vector space for arbitrary independent vectors?

  • kelvin490
  • · Replies 4 ·
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4