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 Possible title: When Does the Kernel of a Homomorphism Reduce to the Identity?

  • TrickyDicky
  • · Replies 5 ·
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5

Undergrad Solutions to Span of Functions Problems

  • gummz
  • · Replies 3 ·
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3

Definitions of Algebras in Cohn and in Golan

  • Math Amateur
  • · Replies 8 ·
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8

Graduate Symmetric Tensor Product in Pic. 1 - Explained

  • mikeeey
  • · Replies 2 ·
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2

Solving Linear Transformations with Matrix A and Vectors u1 & u2

  • AngrySnorlax
  • · Replies 4 ·
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4

Graduate Transform 10 to 1000 Points on x^9 to x^2 Polynomial

  • compEng
  • · Replies 7 ·
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7

Definitions of Algebras in Cohn and in Dummit and Foote

  • Math Amateur
  • · Replies 10 ·
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10

Second Isomorphism Theorem for Groups

  • Math Amateur
  • · Replies 8 ·
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8

Graduate Definition Of Operator Exponential?

  • ostrich2
  • · Replies 3 ·
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3

First Isomorphism Theorem for Modules - Cohn Theorem 1.17

  • Math Amateur
  • · Replies 12 ·
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12

Graduate Why do commuting operators imply that A=A(a) will commute with b?

  • Nikitin
  • · Replies 1 ·
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1

Quotient Modules and Module Homomorphisms - Cohn - Corollary 1.16

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Rules for Multiplying and Adding in Modulo # Calculation

  • MathewsMD
  • · Replies 4 ·
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4

Undergrad Relationship between linear (in)dependency and span

  • gummz
  • · Replies 5 ·
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5

Quotient Modules and Homomorphisms

  • Math Amateur
  • · Replies 3 ·
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3

Modules in Cohn's book on ring theory - simple notational issue

  • Math Amateur
  • · Replies 23 ·
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23

Need help understanding a Lie Algebra

  • topsquark
  • · Replies 7 ·
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7

Graduate Self-adjoint operators and Hermitian operators

  • spaghetti3451
  • · Replies 4 ·
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4

Graduate No Cross Product in higher dimensions?

  • MathewsMD
  • · Replies 5 ·
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5

Graduate Factorizing ##F_{ab}(M)## w/ Respect to Grothendieck Group - Lang's Book

  • xiavatar
  • · Replies 5 ·
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5

Undergrad Linear Algebra Help: Reduce Matrix & Find Error

  • JohnPrior3
  • · Replies 4 ·
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4

Finitely Generated Modules and Ascending Chains

  • Math Amateur
  • · Replies 11 ·
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11

Graduate Number of quadratic residues mod N>1

  • THSMathWhiz
  • · Replies 3 ·
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3

Chains of Modules and Composition Series

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Non-square linear systems with exterior product

  • JonnyMaddox
  • · Replies 1 ·
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1

Graduate Linear operators and vector spaces

  • "Don't panic!"
  • · Replies 5 ·
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5

Noetherian Modules - Cohn Theorem 2.2

  • Math Amateur
  • · Replies 4 ·
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4

Noetherian Modules and Finitely Generated Modules

  • Math Amateur
  • · Replies 2 ·
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2

Are rationals adjoin cube root of 3 a field?

  • Ragnarok7
  • · Replies 3 ·
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3

You're welcome, Peter! I'm glad it was helpful.

  • Math Amateur
  • · Replies 2 ·
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2

Linear Algebras or k-algebras - Cohn p. 53-54 - SIMPLE CLARIFICATION

  • Math Amateur
  • · Replies 10 ·
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10

Graduate Solving the Finite Element Method Matrix with Rao - Engineering

  • Chacabucogod
  • · Replies 3 ·
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3

K-algebras, endomorphisms and k-linear mappings

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Permutations of a group (Understanding Theory)

  • PcumP_Ravenclaw
  • · Replies 17 ·
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17

Regular representations of finite dimensional algebras

  • Math Amateur
  • · Replies 7 ·
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7

Graduate Understanding the Metric Tensor to Tensor Products and Basis Vectors

  • mikeeey
  • · Replies 6 ·
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6

Group Algebra - Cohn page 55 - SIMPLE CLARIFICATION

  • Math Amateur
  • · Replies 3 ·
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3

Noetherian Rings - R Y Sharp - Chapter 8 - exercise 8.5

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Understanding the Inner Product and Dot Product in Linear Algebra

  • jeremusic2
  • · Replies 15 ·
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15

Noetherian Rings - Dummit and Foote - Chapter 15 - exercise 10

  • Math Amateur
  • · Replies 1 ·
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1

Noetherian Rings - Dummit and Foote - Chapter 15

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Does Division of Polynomials Follow a Pattern of Degree Decrease?

  • chwala
  • · Replies 5 ·
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5

Graduate Linear operators and change of basis

  • "Don't panic!"
  • · Replies 2 ·
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2

Graduate 2x2 matrix with factor group elements

  • jostpuur
  • · Replies 2 ·
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2

Graduate How Does kR Equal Zero in Ring Theory?

  • PsychonautQQ
  • · Replies 5 ·
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5

Graduate The deformation of Lie algebra ?

  • Esmaeil
  • · Replies 2 ·
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2

Graduate Partitioning a Group Into Disjoint Subgroups

  • metapuff
  • · Replies 6 ·
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6

Undergrad Linear operators & mappings between vector spaces

  • "Don't panic!"
  • · Replies 8 ·
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8

Graduate Is Associativity Key in Simplifying Multivector Products in Geometric Algebra?

  • JonnyMaddox
  • · Replies 3 ·
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3

Graduate Eigenvalues and eigenvectors of a non-symmetric matrix?

  • prajeesh
  • · Replies 2 ·
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2

Graduate Number of ways to select M cohyperplanar points in finite space

  • Nick O
  • · Replies 4 ·
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4

Graduate Connection between SU(2) and SO(3)

  • HomogenousCow
  • · Replies 8 ·
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8

Quick Question on Modules and Orthogonal Idempotents

  • Math Amateur
  • · Replies 5 ·
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5

Finding subgroups and their generators of cyclic group

  • Ragnarok7
  • · Replies 3 ·
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3

Explicit idempotents - Berrick and Keating - Exercise 2.1.5

  • Math Amateur
  • · Replies 18 ·
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18

Undergrad What does it mean for a set of vectors to be linearly dependent?

  • "Don't panic!"
  • · Replies 15 ·
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15

Endomorphisms of Direct Sums - Berrick and Keating - Exercise 2.1.6 (i)

  • Math Amateur
  • · Replies 7 ·
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7

Bimodules and Endomorphisms - Berrick and Keating - Exercise 1.2.11 page 33

  • Math Amateur
  • · Replies 17 ·
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17

Notation for vector coordinates in a given basis

  • Evgeny.Makarov
  • · Replies 1 ·
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1

Help with B&K Exercise 1.2.11 Pg 33: Bimodules and Endomorphisms

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Mathematical Products: Geometric vs. Tensor

  • mikeeey
  • · Replies 2 ·
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2

Graduate Is -(x^-1) = (-x)^-1 true for all nonzero x in any ring?

  • 1MileCrash
  • · Replies 20 ·
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20

Similar Matrices and Change of Basis

  • Math Amateur
  • · Replies 2 ·
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2

Isomorphism Between Hom_F (V,W) and M_nxn(F) - theory of vector spaces

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad I think I found a flaw in vector combination theory

  • BreezyLeaf
  • · Replies 4 ·
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4

Percolation - Measure - Probability

  • fsblajinha
  • · Replies 1 ·
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1

Bases of functions and Matrices with respect to the bases

  • Kronos1
  • · Replies 5 ·
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5

Undergrad Understanding R₃ in Linear Algebra: A Self-Study Guide

  • abcdefhij
  • · Replies 4 ·
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4

Matrix Rings - Exercise 1.1.4 (iii) - Berrick and Keating (B&K) - page 12

  • Math Amateur
  • · Replies 9 ·
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9

Graduate Weighted Least Squares for coefficients

  • divB
  • · Replies 9 ·
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9

K^n as a K[T]-module - Exercise 1.2.8 (a) - Berrick and Keating (B&K)

  • Math Amateur
  • · Replies 3 ·
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3

Inverse of adjoint - where is my mistake ?

  • Yankel
  • · Replies 3 ·
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3

Graduate How to build a random vector perpendicular to another vector in R3

  • Chandrasekhar
  • · Replies 6 ·
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6

Graduate How Does Hadlock Prove Every Polynomial of Degree n Has a Symmetric Group Sn?

  • Ray
  • · Replies 3 ·
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3

Graduate Singular Value Decomposition: How Can We Efficiently Use SVD Practically?

  • member 428835
  • · Replies 10 ·
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10

Graduate Bases of vector spaces and change of basis

  • "Don't panic!"
  • · Replies 2 ·
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2

Matrix Rings - Exercise 1.1.4 (ii) - Berrick and Keating (B&K) - page 12

  • Math Amateur
  • · Replies 2 ·
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2

Fourth or Lattice Isomorphism Theorem for Modules - clarification

  • Math Amateur
  • · Replies 3 ·
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3

Proof of Fourth or Lattice Isomorphism Theorem for Modules

  • Math Amateur
  • · Replies 2 ·
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2

Modules - Decomposibiity of abelian groups

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Trouble setting up to prove unique factorization

  • lants
  • · Replies 3 ·
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3

Is Matrix A Invertible Given (AB)C Equals the Identity Matrix?

  • Yankel
  • · Replies 5 ·
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5

System of linear equations, all possible outcomes

  • Yankel
  • · Replies 5 ·
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5

K^n as a K[T]-module - Example 2.1.2

  • Math Amateur
  • · Replies 3 ·
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3

Graduate How Is the Killing Metric Normalized for Compact Simple Groups?

  • center o bass
  • · Replies 2 ·
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2

Graduate Finding Lie-Algebra Invariants -- an Explicit Procedure?

  • lpetrich
  • · Replies 1 ·
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1

Graduate What is the connection between 2-forms, determinants, and cross products in R^3?

  • JonnyMaddox
  • · Replies 1 ·
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1

Indecomposable modules - example from Berrick and Keating

  • Math Amateur
  • · Replies 4 ·
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4

Find matrix representation with respect to the basis

  • Kronos1
  • · Replies 4 ·
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4

Graduate Ring Theory Problems: Unity vs. Non-Unity

  • gianeshwar
  • · Replies 3 ·
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3

Undergrad Decompose a Recipe into Its Constituent Ingredients

  • Rocky9242
  • · Replies 3 ·
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3

Definition of Direct Product Using UMP - Including Infinite Case

  • Math Amateur
  • · Replies 18 ·
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18

Undergrad Why Fields are Necessary for Linear Algebra

  • timkuc
  • · Replies 10 ·
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10

Using the given basis of a vector to prove other basis

  • Kronos1
  • · Replies 1 ·
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1

Graduate Understanding Adjoint Operators: A Helpful Explanation and Example

  • member 428835
  • · Replies 10 ·
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10

Undergrad Are Slack Variables Causing Infeasible Points in Simplex Method?

  • liquidFuzz
  • · Replies 10 ·
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10

Graduate Converting an explicit series to a recursive form

  • regina_lee
  • · Replies 2 ·
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2

Undergrad Fast tridiagonal matrix algorithm

  • ShayanJ
  • · Replies 2 ·
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2

Infinite Direct Sums and Indexed Sets

  • Math Amateur
  • · Replies 9 ·
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9

Graduate Inhomogeneous Linear System Solutions

  • GregJ
  • · Replies 1 ·
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1