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.
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Undergrad Free Modules, Bases and Direct Sums/Products
- Math Amateur
- · Replies 17 ·
Undergrad Prove an nth-degree polynomial has exactly n roots
- Happiness
- · Replies 3 ·
What Is the Structure of Modules Over Polynomial Rings?
- mathmari
- · Replies 1 ·
High School Does the L2 norm of a vector destroy all directional info?
- phasic
- · Replies 6 ·
Undergrad Don't understand lemma about primitive polynomial product
- swampwiz
- · Replies 8 ·
Undergrad Cramer's Rule and Dyadics(Menzel)
- Odious Suspect
- · Replies 4 ·
Undergrad Square of determinant is symmetric
- debjit625
- · Replies 8 ·
Total Labor Cost Per Good Matrix Calculation
- Binte
- · Replies 1 ·
A subset of R^(2) that is a nontrivial subspace of R^(2)
- Zoey93
- · Replies 18 ·
Tensor Products of Modules and Free Abelian Groups based on Cartesian Product
- Math Amateur
- · Replies 2 ·
Undergrad Linear dependency of Vectors above R and C and the det
- Dank2
- · Replies 5 ·
Linear Algebra Expert Requested For Discussion
- bwpbruce
- · Replies 2 ·
Undergrad Isolate variables in nonlinear equation for regression
- edge333
- · Replies 2 ·
Undergrad Are f(x) = xcos(x) and g(x) = cos(x) Linearly Independent?
- Dank2
- · Replies 22 ·
Undergrad Free Abelian Groups .... Aluffi Proposition 5.6
- Math Amateur
- · Replies 40 ·
Undergrad Group Normalcy not transitive example?
- PsychonautQQ
- · Replies 7 ·
Undergrad How Can a Set Fail the Scalar Identity Axiom in Vector Spaces?
- elements
- · Replies 1 ·
Are Hom_R(R, M) and M Isomorphic?
- mathmari
- · Replies 3 ·
Free Abelian Groups .... Aluffi Proposition 5.6
- Math Amateur
- · Replies 4 ·
Prove $R$ is a Field: Finitely Generated Modules are Free
- mathmari
- · Replies 5 ·
Proving $M$ is Cyclic: Simple $R$-Module & Isomorphism with Maximal Ideal $J$
- mathmari
- · Replies 20 ·
Did I Make an Error in My Euclidean Division Calculation?
- evinda
- · Replies 14 ·
Undergrad Can Linear Programming Handle Combined Item and Shipping Costs Optimization?
- lavoisier
- · Replies 7 ·
How can we conclude from that that I is a principal ideal?
- mathmari
- · Replies 1 ·
Exploring the Periodicity of Powers in Modular Arithmetic
- Evgeny.Makarov
- · Replies 16 ·
The endomorphism ring is a field
- mathmari
- · Replies 3 ·
How to Find the Product of Cyclic Groups in an Abelian Group?
- mathmari
- · Replies 5 ·
What Should Computer Science Majors Expect from Linear Algebra?
- suluclac
- · Replies 1 ·
Undergrad General form of symmetric 3x3 matrix with only 2 eigenvalues
- odietrich
- · Replies 4 ·
Is φ a bijective homomorphism between simple $R$-modules?
- mathmari
- · Replies 3 ·
What Are the Prime and Maximal Ideals in the Ring $\mathbb{Z}_{12}$?
- mathmari
- · Replies 9 ·
An Artinian integral domain is a field
- mathmari
- · Replies 4 ·
The principal ideal is maximal in but it is not the unique maximal ideal
- mathmari
- · Replies 21 ·
Undergrad Can we add two vectors that are not acting simultaneously using vector addition?
- prashant singh
- · Replies 11 ·
Unique Automorphism of R[x] - A Hint for Invertible a & b
- mathmari
- · Replies 23 ·
Undergrad About Lie group product ([itex]U(1)\times U(1)[/itex] ex.)
- guest1234
- · Replies 1 ·
Undergrad Multiplication by a matrix in GL rotates a plane's basis?
- joej24
- · Replies 2 ·
Categories of Pointed Sets - Aluffi, Example 3.8
- Math Amateur
- · Replies 5 ·
Undergrad Is There Proof for the Cross Product Matrix Formula?
- prashant singh
- · Replies 6 ·
Closure under Scalar multiplication
- Zoey93
- · Replies 3 ·
Undergrad How can we determine if D3xZ2 contains an element of order 6?
- spacetimedude
- · Replies 9 ·
Graduate Question about properites of tensor product
- td21
- · Replies 1 ·
Undergrad Taking the Tensor Product of Vectors
- JonnyG
- · Replies 1 ·
Undergrad Cross product or vector product.
- prashant singh
- · Replies 5 ·
Undergrad Why does A.A = ||A||^2 in the scalar product formula?
- prashant singh
- · Replies 13 ·
Undergrad Vectors Cartesian equations and normals
- 53Mark53
- · Replies 10 ·
Undergrad Categories of Pointed Sets - Aluffi, Example 3.8
- Math Amateur
- · Replies 4 ·
Tensor Algebras and Graded Algebras - Cooperstein - Theorem 10.11 and Defn 10.7
- Math Amateur
- · Replies 2 ·
Undergrad Scalar product and vector product
- prashant singh
- · Replies 5 ·
Undergrad Vector equation perpendicular to two equations
- 53Mark53
- · Replies 10 ·
Undergrad Matrix Representation of Linear Transformation
- KT KIM
- · Replies 3 ·
Undergrad Which Are the EOFs in SVD?
- ecastro
- · Replies 1 ·
Undergrad Does this concept have a name? (looping/overlapping time)
- Masontc
- · Replies 2 ·
Undergrad Tensor Algebras and Graded Algebras - Cooperstein
- Math Amateur
- · Replies 2 ·
Undergrad How do we divide one vector field by another?
- tade
- · Replies 4 ·
Symmetry in the algebraic expressions
- NotaMathPerson
- · Replies 2 ·
Undergrad The Tensor Algebra - Cooperstein, Defn 10.5
- Math Amateur
- · Replies 11 ·
Tensor Algebras - Dummit and Foote, Section 11.5
- Math Amateur
- · Replies 3 ·
Undergrad Tensor Algebras - Dummit and Foote, Section 11.5
- Math Amateur
- · Replies 7 ·
Undergrad Exponential Operators: Inverting, Rearranging, Expanding
- dyn
- · Replies 3 ·
Undergrad What is the outer product of a tensor product of vectors?
- Frank Castle
- · Replies 5 ·
Undergrad The Tensor Algebra - Cooperstein, Example 10.1
- Math Amateur
- · Replies 4 ·
Tensor Algebras - Cooperstein Example 10.1
- Math Amateur
- · Replies 1 ·
Tensor Products and Associative Algebras
- Math Amateur
- · Replies 1 ·
Undergrad Stupid Question about a Notation in Linear algebra
- smodak
- · Replies 6 ·
Undergrad How this defines a linear transformation
- Granger
- · Replies 3 ·
How to define this linear transformation
- Granger
- · Replies 1 ·
Undergrad Finding the matrix inverse by diagonalisation
- Physgeek64
- · Replies 2 ·
Galois Groups and Minimum Polynomial
- mathjam0990
- · Replies 1 ·
Tensor Algebras - Cooperstein Theorem 10.8
- Math Amateur
- · Replies 7 ·
Graduate Definition of observability indices?
- james1234
- · Replies 1 ·
Undergrad Tensor Algebras - Cooperstein Theorem 10.8
- Math Amateur
- · Replies 10 ·
Relationship between metric and inner product
- dingo
- · Replies 1 ·
Graduate Understanding the Connection Between Lie Algebras and Rotations
- observer1
- · Replies 8 ·
Characterization of External Direct Sum - Cooperstein, pages 359 - 360
- Math Amateur
- · Replies 1 ·
Tensor Products - Basic Understanding of Cooperstein, Theorem 10.2
- Math Amateur
- · Replies 2 ·
Undergrad What's the Difference Between Zero Divisors and Torsion Elements?
- CSteiner
- · Replies 5 ·
Undergrad Cosets: Is [gH] a Subgroup of G?
- Clear Mind
- · Replies 5 ·
Undergrad Tensor Products - Understanding Cooperstein, Theorem 10.2
- Math Amateur
- · Replies 1 ·
Undergrad Adjoint representation and the generators
- CAF123
- · Replies 10 ·
Undergrad Can Normal Matrices Be Non-Self-Adjoint?
- tommyxu3
- · Replies 5 ·
Undergrad Characterization of External Direct Sum - Cooperstein
- Math Amateur
- · Replies 2 ·
Undergrad Some questions about eigenvector computation
- swampwiz
- · Replies 4 ·
Undergrad Extension of scalars .... D&F, Section 10.4: Tensor Products
- Math Amateur
- · Replies 7 ·
Undergrad Group Theory: Unlocking Real-World Solutions for First-Year Students
- matqkks
- · Replies 7 ·
Proof of Existence of Tensor Product .... Cooperstein ....
- Math Amateur
- · Replies 13 ·
High School Algebra question -- Solving 2 simultaneous equations....
- Biker
- · Replies 6 ·
Is R a Principal Ideal Domain (P.I.D) Given These Properties?
- mathmari
- · Replies 3 ·
Undergrad Confused about basis vector notation
- snoopies622
- · Replies 4 ·
Show Finite Principal Ideals Contain $(d)$ in U.F.D.
- mathmari
- · Replies 2 ·
Undergrad Commutator between Casimirs and generators for Lorentz group
- julian
- · Replies 5 ·
Is $I$ an Ideal in a Ring $R$?
- mathmari
- · Replies 5 ·
How can we show that a has a left inverse?
- mathmari
- · Replies 12 ·
Is $1-y$ always lacking a right inverse when $y$ is a non-unit in a right ideal?
- mathmari
- · Replies 8 ·
Graduate Equation with three consecutive prime numbers
- Dacu
- · Replies 2 ·
Undergrad How to Solve for a 3x3 Matrix Using A and B Vectors?
- DivGradCurl
- · Replies 8 ·
Undergrad Third Invariant expressed with Cayley-Hamilton Theorem
- FluidStu
- · Replies 2 ·
Extension of Scalars: Dummit & Foote's Section 10.4 Q&A
- Math Amateur
- · Replies 8 ·
Automorphisms, Galois Groups & Splitting Fields
- mathjam0990
- · Replies 3 ·
P-Adic Localization in Rational Numbers: A Proof of Local Subring Property
- mathmari
- · Replies 1 ·