Linear and Abstract Algebra Forum

Post thread
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.
MHB (x) and (x,y) are prime ideals of Q[x,y]
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Tensor Products of Modules - Bland - Remark, Page 65
  • · Replies 4 ·
Replies
4
Views
2K
MHB Tensor Products of Modules - Bland - Remark, Page 65
  • · Replies 1 ·
Replies
1
Views
2K
MHB Tensor Products and the Free Z-module - Bland Propostion 2.2.3 .... ....
  • · Replies 3 ·
Replies
3
Views
1K
MHB Understanding Bland's Example: Free Modules & Directly Finite/Infinite R-Modules
  • · Replies 7 ·
Replies
7
Views
2K
MHB These are the only submodule
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Multiple time derivatives of gravitational potential
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Spherical coordinates via a rotation matrix
  • · Replies 3 ·
Replies
3
Views
10K
Undergrad What kind of space is the space of spinors?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Eigenspectra and Empirical Orthogonal Functions
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Directly Finite and Directly Infinite R-Modules - Bland S2.2
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Same vector space for arbitrary independent vectors?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Free Modules, Bases and Direct Sums/Products
  • · Replies 17 ·
Replies
17
Views
3K
MHB What Is the Structure of Modules Over Polynomial Rings?
  • · Replies 1 ·
Replies
1
Views
1K
High School Does the L2 norm of a vector destroy all directional info?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Cramer's Rule and Dyadics(Menzel)
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Square of determinant is symmetric
  • · Replies 8 ·
Replies
8
Views
4K
MHB Total Labor Cost Per Good Matrix Calculation
  • · Replies 1 ·
Replies
1
Views
1K
MHB A subset of R^(2) that is a nontrivial subspace of R^(2)
  • · Replies 18 ·
Replies
18
Views
6K
MHB Tensor Products of Modules and Free Abelian Groups based on Cartesian Product
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Linear dependency of Vectors above R and C and the det
  • · Replies 5 ·
Replies
5
Views
1K
MHB Linear Algebra Expert Requested For Discussion
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Isolate variables in nonlinear equation for regression
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Are f(x) = xcos(x) and g(x) = cos(x) Linearly Independent?
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Free Abelian Groups .... Aluffi Proposition 5.6
  • · Replies 40 ·
2
Replies
40
Views
5K
Undergrad Group Normalcy not transitive example?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad How Can a Set Fail the Scalar Identity Axiom in Vector Spaces?
  • · Replies 1 ·
Replies
1
Views
3K
MHB Are Hom_R(R, M) and M Isomorphic?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Free Abelian Groups .... Aluffi Proposition 5.6
  • · Replies 4 ·
Replies
4
Views
2K
MHB Prove $R$ is a Field: Finitely Generated Modules are Free
  • · Replies 5 ·
Replies
5
Views
2K
MHB Proving $M$ is Cyclic: Simple $R$-Module & Isomorphism with Maximal Ideal $J$
  • · Replies 20 ·
Replies
20
Views
4K
Undergrad Can Linear Programming Handle Combined Item and Shipping Costs Optimization?
  • · Replies 7 ·
Replies
7
Views
2K
MHB How can we conclude from that that I is a principal ideal?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Exploring the Periodicity of Powers in Modular Arithmetic
  • · Replies 16 ·
Replies
16
Views
5K
MHB The endomorphism ring is a field
  • · Replies 3 ·
Replies
3
Views
2K
MHB How to Find the Product of Cyclic Groups in an Abelian Group?
  • · Replies 5 ·
Replies
5
Views
2K
MHB What Should Computer Science Majors Expect from Linear Algebra?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad General form of symmetric 3x3 matrix with only 2 eigenvalues
  • · Replies 4 ·
Replies
4
Views
6K
MHB Is φ a bijective homomorphism between simple $R$-modules?
  • · Replies 3 ·
Replies
3
Views
2K
MHB What Are the Prime and Maximal Ideals in the Ring $\mathbb{Z}_{12}$?
  • · Replies 9 ·
Replies
9
Views
3K
MHB An Artinian integral domain is a field
  • · Replies 4 ·
Replies
4
Views
2K
MHB The principal ideal is maximal in but it is not the unique maximal ideal
  • · Replies 21 ·
Replies
21
Views
4K
MHB Unique Automorphism of R[x] - A Hint for Invertible a & b
  • · Replies 23 ·
Replies
23
Views
3K
Undergrad About Lie group product ([itex]U(1)\times U(1)[/itex] ex.)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Multiplication by a matrix in GL rotates a plane's basis?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Categories of Pointed Sets - Aluffi, Example 3.8
  • · Replies 5 ·
Replies
5
Views
2K
MHB Closure under Scalar multiplication
  • · Replies 3 ·
Replies
3
Views
8K
Undergrad How can we determine if D3xZ2 contains an element of order 6?
  • · Replies 9 ·
Replies
9
Views
4K
Graduate Question about properites of tensor product
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Taking the Tensor Product of Vectors
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Categories of Pointed Sets - Aluffi, Example 3.8
  • · Replies 4 ·
Replies
4
Views
2K
MHB Tensor Algebras and Graded Algebras - Cooperstein - Theorem 10.11 and Defn 10.7
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Matrix Representation of Linear Transformation
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Which Are the EOFs in SVD?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Does this concept have a name? (looping/overlapping time)
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Tensor Algebras and Graded Algebras - Cooperstein
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How do we divide one vector field by another?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad The Tensor Algebra - Cooperstein, Defn 10.5
  • · Replies 11 ·
Replies
11
Views
2K
MHB Tensor Algebras - Dummit and Foote, Section 11.5
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Tensor Algebras - Dummit and Foote, Section 11.5
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Exponential Operators: Inverting, Rearranging, Expanding
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What is the outer product of a tensor product of vectors?
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad The Tensor Algebra - Cooperstein, Example 10.1
  • · Replies 4 ·
Replies
4
Views
2K
MHB Tensor Algebras - Cooperstein Example 10.1
  • · Replies 1 ·
Replies
1
Views
1K
MHB Tensor Products and Associative Algebras
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Stupid Question about a Notation in Linear algebra
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How this defines a linear transformation
  • · Replies 3 ·
Replies
3
Views
1K
MHB How to define this linear transformation
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Finding the matrix inverse by diagonalisation
  • · Replies 2 ·
Replies
2
Views
2K
MHB Galois Groups and Minimum Polynomial
  • · Replies 1 ·
Replies
1
Views
1K
MHB Tensor Algebras - Cooperstein Theorem 10.8
  • · Replies 7 ·
Replies
7
Views
2K
Definition of observability indices?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Tensor Algebras - Cooperstein Theorem 10.8
  • · Replies 10 ·
Replies
10
Views
2K
MHB Relationship between metric and inner product
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Understanding the Connection Between Lie Algebras and Rotations
  • · Replies 8 ·
Replies
8
Views
3K
MHB Characterization of External Direct Sum - Cooperstein, pages 359 - 360
  • · Replies 1 ·
Replies
1
Views
1K
MHB Tensor Products - Basic Understanding of Cooperstein, Theorem 10.2
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What's the Difference Between Zero Divisors and Torsion Elements?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Cosets: Is [gH] a Subgroup of G?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Tensor Products - Understanding Cooperstein, Theorem 10.2
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Adjoint representation and the generators
  • · Replies 10 ·
Replies
10
Views
4K
Undergrad Can Normal Matrices Be Non-Self-Adjoint?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Characterization of External Direct Sum - Cooperstein
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Some questions about eigenvector computation
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Extension of scalars .... D&F, Section 10.4: Tensor Products
  • · Replies 7 ·
Replies
7
Views
2K
MHB Proof of Existence of Tensor Product .... Cooperstein ....
  • · Replies 13 ·
Replies
13
Views
3K
MHB Is R a Principal Ideal Domain (P.I.D) Given These Properties?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Confused about basis vector notation
  • · Replies 4 ·
Replies
4
Views
3K
MHB Show Finite Principal Ideals Contain $(d)$ in U.F.D.
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Commutator between Casimirs and generators for Lorentz group
  • · Replies 5 ·
Replies
5
Views
2K
MHB Is $I$ an Ideal in a Ring $R$?
  • · Replies 5 ·
Replies
5
Views
2K
MHB How can we show that a has a left inverse?
  • · Replies 12 ·
Replies
12
Views
3K
MHB Is $1-y$ always lacking a right inverse when $y$ is a non-unit in a right ideal?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Equation with three consecutive prime numbers
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Third Invariant expressed with Cayley-Hamilton Theorem
  • · Replies 2 ·
Replies
2
Views
2K
MHB Extension of Scalars: Dummit & Foote's Section 10.4 Q&A
  • · Replies 8 ·
Replies
8
Views
3K
MHB Automorphisms, Galois Groups & Splitting Fields
  • · Replies 3 ·
Replies
3
Views
3K
MHB P-Adic Localization in Rational Numbers: A Proof of Local Subring Property
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Eigen Vectors, Geometric Multiplicities and more....
  • · Replies 5 ·
Replies
5
Views
2K
MHB Is Every Non-Zero Element in a Finite Ring Invertible?
  • · Replies 23 ·
Replies
23
Views
4K