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 A decreasing sequence of images of an endomorphisme

  • steenis
  • · Replies 18 ·
Replies
18

Graduate If U is closed under * in V=U⊕W, is W also closed?

  • mnb96
  • · Replies 3 ·
Replies
3

Direct Sums and Factor Modules .... Bland Problem 14, Problem Set 2.1

  • Math Amateur
  • · Replies 8 ·
Replies
8

Max Complex Matrices of Order $n$: $\lfloor n^2/4\rfloor + 1$

  • MountEvariste
  • · Replies 2 ·
Replies
2

Artinian modules in Cohn's ring theory textbook

  • Math Amateur
  • · Replies 10 ·
Replies
10

Start on Bland Problem 1, Problem Set 4.1: Generating & Cogenerating Modules

  • Math Amateur
  • · Replies 37 ·
2
Replies
37

Graduate Finitely generated submodule of direct sum of modules

  • steenis
  • · Replies 7 ·
Replies
7

On a finiteley generated submodule of a direct sum of left R-modules

  • steenis
  • · Replies 1 ·
Replies
1
Replies
10

Undergrad External direct sums and sum of families of mappings in Bland

  • Math Amateur
  • · Replies 4 ·
Replies
4

Graduate Infinite matrices and the Trace function

  • LagrangeEuler
  • · Replies 3 ·
Replies
3

Undergrad Coordinate systems in ##\mathbb{R}^2##

  • kent davidge
  • · Replies 27 ·
Replies
27

Undergrad Finitely Generated Modules and Maximal Submodules

  • Math Amateur
  • · Replies 3 ·
Replies
3

Equivalent Norms: Proving $\|A\| \leq \|A\|_{Eucl} \leq \sqrt{n}\|A\|$

  • mathmari
  • · Replies 4 ·
Replies
4

Undergrad Noetherian Modules and Submodules

  • Math Amateur
  • · Replies 15 ·
Replies
15

Undergrad Noetherian Modules - Bland, Example 3, Section 4.2 ....

  • Math Amateur
  • · Replies 4 ·
Replies
4

Noetherian Modules - Bland, Example 3, Section 4.2 ....

  • Math Amateur
  • · Replies 6 ·
Replies
6

Proving Identities Using Axioms of Equality

  • solakis1
  • · Replies 16 ·
Replies
16

Short Exact Sequences and Direct Sums .... Bland, Proposition 3.2.7 .... ....

  • Math Amateur
  • · Replies 2 ·
Replies
2

Are These Polynomial Factorizations Correct in Z7?

  • ertagon2
  • · Replies 4 ·
Replies
4

Undergrad Short Exact Sequences & Direct Sums .... Bland, Proposition 3.2.7

  • Math Amateur
  • · Replies 25 ·
Replies
25

Plane velocity with wind using vector components

  • JRoomer
  • · Replies 1 ·
Replies
1

Undergrad Understanding Z2 Graded Vector Spaces: Definition and Examples

  • Silviu
  • · Replies 3 ·
Replies
3

Undergrad Split epimorphisms in Bland's Rings and Their Modules

  • Math Amateur
  • · Replies 4 ·
Replies
4

Proposition 3.2.6 in Bland's Rings and Their Modules

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Split Short Exact Sequences .... Bland, Proposition 3.2.6 ....

  • Math Amateur
  • · Replies 3 ·
Replies
3

Does Proposition 3.2.6 Imply g'(y) = x' - f(f'(x'))?

  • Math Amateur
  • · Replies 1 ·
Replies
1

Split epimorphisms in Bland's Rings and Their Modules

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad How to Write the Inverse of a Matrix Using Einstein Summation Notation?

  • Mathematicsresear
  • · Replies 5 ·
Replies
5

Graduate Hermitian Operators and Projectors in Linear Algebra

  • LagrangeEuler
  • · Replies 2 ·
Replies
2

Undergrad Split monomorphisms in Bland definition 3.2.2

  • Math Amateur
  • · Replies 5 ·
Replies
5

Split monomorphism in Bland's Rings and Modules 3.2.2

  • Math Amateur
  • · Replies 2 ·
Replies
2

Free Modules, Bases and Direct Sums/Products - Bland, Proposition 2.2.3

  • Math Amateur
  • · Replies 5 ·
Replies
5

Right ideals of ring direct products are direct products

  • Math Amateur
  • · Replies 8 ·
Replies
8

Undergrad Eigenproblem for non-normal matrix

  • swampwiz
  • · Replies 5 ·
Replies
5

Direct sum of finitely generated modules is finitely generated

  • Math Amateur
  • · Replies 1 ·
Replies
1

Understanding Determinants of 2 x 2 Matrices

  • ertagon2
  • · Replies 1 ·
Replies
1

Irreducible Polynomial g = X^4 + X + 1 over F2

  • aadams
  • · Replies 3 ·
Replies
3

Undergrad Understand homomorphisms from Z^a --> Z^b

  • PsychonautQQ
  • · Replies 1 ·
Replies
1

Find position vector using midpoint of two other vectors

  • TheFallen018
  • · Replies 1 ·
Replies
1

Undergrad Inverse of the sum of two matrices

  • Luck0
  • · Replies 4 ·
Replies
4

Undergrad What is difference between transformations and automorphisms

  • SVN
  • · Replies 5 ·
Replies
5

Undergrad Linear Programming: how to identify conflicting equations

  • cjs94
  • · Replies 2 ·
Replies
2

How to Compute Matrix Powers with Sage

  • karush
  • · Replies 7 ·
Replies
7

Graduate Are Eigenvalues of Hermitian Integer Matrices Always Integers?

  • LagrangeEuler
  • · Replies 3 ·
Replies
3

Undergrad Why Is Reflection in a Hyperplane a Linear Function?

  • Aleoa
  • · Replies 3 ·
Replies
3

Proving product equals direct sum iff index set is finite

  • Math Amateur
  • · Replies 17 ·
Replies
17

Is the direct sum a right ideal of the direct product of rings?

  • Math Amateur
  • · Replies 1 ·
Replies
1

Is \(\bigoplus_\Delta A_\alpha\) a Right Ideal of \(\prod_\Delta R_\alpha\)?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad How Do SU(2) and SO(3) Relate to Spinors and Vectors in Physics?

  • Silviu
  • · Replies 11 ·
Replies
11

Graduate Solve Badly Scaled Problem with Newton-Chord Technique

  • Ulver48
  • · Replies 12 ·
Replies
12

Product of right ideals is a right ideal in Bland section 2.1

  • Math Amateur
  • · Replies 2 ·
Replies
2

Understanding Categories: A Question on Commutativity

  • topsquark
  • · Replies 6 ·
Replies
6

High School What does î(o) represent in vectors?

  • Kavya Chopra
  • · Replies 7 ·
Replies
7

Undergrad Astrodynamics Question: Derivation of Sp. Orbital Energy?

  • AdrianGriff
  • · Replies 3 ·
Replies
3

Undergrad Difference between R^n and other vector spaces

  • Mr Davis 97
  • · Replies 2 ·
Replies
2

Undergrad Why is u_α injective in Bland's Proposition 2.1.4 on direct products?

  • Math Amateur
  • · Replies 12 ·
Replies
12

How Is u_alpha an Injective Mapping in Proposition 2.1.4?

  • Math Amateur
  • · Replies 4 ·
Replies
4

Undergrad Orbits of Z/6Z under cyclic permutation and 2-element subsets

  • mk9898
  • · Replies 3 ·
Replies
3

Undergrad Where R-linearity is used in Bland's Proposition 2.1.1 on direct products

  • Math Amateur
  • · Replies 4 ·
Replies
4

Why R-linear property matters in Bland's Proposition 2.1.1 on direct products

  • Math Amateur
  • · Replies 4 ·
Replies
4

Finding congruence solutions in F[x] and checking my work

  • Joe20
  • · Replies 1 ·
Replies
1

Ideals and Ker(f) Solution for (a), (b), and (c)

  • Joe20
  • · Replies 12 ·
Replies
12

High School How does matrix non-commutivity relate to eigenvectors?

  • snoopies622
  • · Replies 26 ·
Replies
26

Undergrad Understanding SU(2) and SO(3) Representations

  • Silviu
  • · Replies 4 ·
Replies
4

Proof of Proposition 2.1.1 in Bland's Rings and Modules

  • Math Amateur
  • · Replies 1 ·
Replies
1

Undergrad Uniqueness in Proposition 2.1.1 on direct products of modules

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Can You Add a Scalar to a Matrix Directly?

  • Danijel
  • · Replies 2 ·
Replies
2

Right annihilator of R/m in Bland Proposition 6.1.7

  • Math Amateur
  • · Replies 1 ·
Replies
1

Homogeneous, underdetermined equation system

  • ToastIQ
  • · Replies 9 ·
Replies
9

Undergrad What are the best resources for learning about Lorentz group representations?

  • Silviu
  • · Replies 1 ·
Replies
1

Undergrad Proving only 1 normalized unitary vector for normal matrix

  • swampwiz
  • · Replies 3 ·
Replies
3

What is the determinant of a 3x3 matrix using various methods?

  • karush
  • · Replies 2 ·
Replies
2

Noetherian Rings and Modules: Theorem 2.2 - Cohn - Section 2.2 Chain Conditions

  • Math Amateur
  • · Replies 3 ·
Replies
3

Cohn Theorem 2.2: why equality holds in chain from N_k onwards

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Proof of Theorem 2.2 on Noetherian modules in Cohn

  • Math Amateur
  • · Replies 3 ·
Replies
3

Theorem 3.1.4 - Berrick and Keating - Noetherian Rings and Modules

  • Math Amateur
  • · Replies 2 ·
Replies
2

Noetherian Modules - Maximal Condition - Berrick and Keating Ch. 3, page 111

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad How to model and resolve a static non-interpenetration constraint

  • fermipasta
  • · Replies 1 ·
Replies
1

How Do You Find the Inverse of a Matrix Using the Adjoint Method?

  • karush
  • · Replies 15 ·
Replies
15

Undergrad Why is the Z-module action on an abelian group unique?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Z-module actions and uniqueness in Dummit & Foote

  • Math Amateur
  • · Replies 1 ·
Replies
1

Undergrad Linear mapping of a binary vector based on its decimal value

  • smehdi
  • · Replies 6 ·
Replies
6

Why (R/I)-modules require am=0 for all a in I and m in M

  • Math Amateur
  • · Replies 8 ·
Replies
8

Undergrad Why (R/I)-modules require am = 0 for all a in I

  • Math Amateur
  • · Replies 7 ·
Replies
7

High School Build an affine/vector space for physics

  • Aleoa
  • · Replies 13 ·
Replies
13

Correspondence Theorem surjectivity proof in Rotman chapter 1

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Correspondence theorem for groups: preimage properties and surjectivity

  • Math Amateur
  • · Replies 5 ·
Replies
5

Undergrad Why does π(a) = π(s) imply as⁻¹ ∈ ker π in Rotman 1.82?

  • Math Amateur
  • · Replies 5 ·
Replies
5

Proving as⁻¹ ∈ ker π in Rotman Proposition 1.82

  • Math Amateur
  • · Replies 2 ·
Replies
2

Understanding Null Space and Column Space of a Matrix

  • karush
  • · Replies 4 ·
Replies
4
Replies
3

Convergence of iteration method - Relation between norm and eigenvalue

  • mathmari
  • · Replies 2 ·
Replies
2

Undergrad Normalized basis when taking inner product

  • kent davidge
  • · Replies 4 ·
Replies
4
Replies
5
Replies
1

Why is f an epimorphism in Bland's third isomorphism theorem for rings?

  • Math Amateur
  • · Replies 3 ·
Replies
3

Undergrad Why is f onto (I₁+I₂)/I₂ in Bland's third isomorphism theorem for rings?

  • Math Amateur
  • · Replies 2 ·
Replies
2

Undergrad Kernel of homomorphism in second isomorphism theorem for rings

  • Math Amateur
  • · Replies 4 ·
Replies
4

Verify my polynomial proof

  • Joe20
  • · Replies 1 ·
Replies
1