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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 Definitions of Algebras in Cohn and in Dummit and Foote
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MHB Second Isomorphism Theorem for Groups
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Graduate Definition Of Operator Exponential?
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MHB First Isomorphism Theorem for Modules - Cohn Theorem 1.17
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Graduate Why do commuting operators imply that A=A(a) will commute with b?
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MHB Quotient Modules and Module Homomorphisms - Cohn - Corollary 1.16
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Undergrad Rules for Multiplying and Adding in Modulo # Calculation
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Undergrad Relationship between linear (in)dependency and span
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MHB Quotient Modules and Homomorphisms
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MHB Modules in Cohn's book on ring theory - simple notational issue
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MHB Need help understanding a Lie Algebra
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Graduate Self-adjoint operators and Hermitian operators
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Graduate No Cross Product in higher dimensions?
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Graduate Factorizing ##F_{ab}(M)## w/ Respect to Grothendieck Group - Lang's Book
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Undergrad Linear Algebra Help: Reduce Matrix & Find Error
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MHB Finitely Generated Modules and Ascending Chains
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Graduate Number of quadratic residues mod N>1
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MHB Chains of Modules and Composition Series
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Graduate Non-square linear systems with exterior product
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Graduate Linear operators and vector spaces
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MHB Noetherian Modules - Cohn Theorem 2.2
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MHB Noetherian Modules and Finitely Generated Modules
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MHB Are rationals adjoin cube root of 3 a field?
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MHB You're welcome, Peter! I'm glad it was helpful.
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MHB Linear Algebras or k-algebras - Cohn p. 53-54 - SIMPLE CLARIFICATION
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Graduate Solving the Finite Element Method Matrix with Rao - Engineering
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MHB K-algebras, endomorphisms and k-linear mappings
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Graduate Permutations of a group (Understanding Theory)
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MHB Regular representations of finite dimensional algebras
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Graduate Understanding the Metric Tensor to Tensor Products and Basis Vectors
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MHB Group Algebra - Cohn page 55 - SIMPLE CLARIFICATION
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MHB Noetherian Rings - R Y Sharp - Chapter 8 - exercise 8.5
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Undergrad Understanding the Inner Product and Dot Product in Linear Algebra
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MHB Noetherian Rings - Dummit and Foote - Chapter 15 - exercise 10
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MHB Noetherian Rings - Dummit and Foote - Chapter 15
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Undergrad Does Division of Polynomials Follow a Pattern of Degree Decrease?
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Graduate Linear operators and change of basis
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Graduate 2x2 matrix with factor group elements
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Graduate How Does kR Equal Zero in Ring Theory?
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Graduate The deformation of Lie algebra ?
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Graduate Partitioning a Group Into Disjoint Subgroups
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Undergrad Linear operators & mappings between vector spaces
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Graduate Is Associativity Key in Simplifying Multivector Products in Geometric Algebra?
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Graduate Eigenvalues and eigenvectors of a non-symmetric matrix?
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Graduate Number of ways to select M cohyperplanar points in finite space
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Graduate Connection between SU(2) and SO(3)
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MHB Quick Question on Modules and Orthogonal Idempotents
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MHB Finding subgroups and their generators of cyclic group
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MHB Explicit idempotents - Berrick and Keating - Exercise 2.1.5
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Undergrad What does it mean for a set of vectors to be linearly dependent?
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MHB Endomorphisms of Direct Sums - Berrick and Keating - Exercise 2.1.6 (i)
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MHB Bimodules and Endomorphisms - Berrick and Keating - Exercise 1.2.11 page 33
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MHB Notation for vector coordinates in a given basis
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MHB Help with B&K Exercise 1.2.11 Pg 33: Bimodules and Endomorphisms
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Undergrad Mathematical Products: Geometric vs. Tensor
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Graduate Is -(x^-1) = (-x)^-1 true for all nonzero x in any ring?
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MHB Similar Matrices and Change of Basis
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MHB Isomorphism Between Hom_F (V,W) and M_nxn(F) - theory of vector spaces
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Undergrad I think I found a flaw in vector combination theory
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MHB Percolation - Measure - Probability
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MHB Bases of functions and Matrices with respect to the bases
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Undergrad Understanding R₃ in Linear Algebra: A Self-Study Guide
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MHB Matrix Rings - Exercise 1.1.4 (iii) - Berrick and Keating (B&K) - page 12
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Graduate Weighted Least Squares for coefficients
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MHB K^n as a K[T]-module - Exercise 1.2.8 (a) - Berrick and Keating (B&K)
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MHB Inverse of adjoint - where is my mistake ?
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Graduate How to build a random vector perpendicular to another vector in R3
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Graduate How Does Hadlock Prove Every Polynomial of Degree n Has a Symmetric Group Sn?
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Graduate Singular Value Decomposition: How Can We Efficiently Use SVD Practically?
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Graduate Bases of vector spaces and change of basis
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MHB Matrix Rings - Exercise 1.1.4 (ii) - Berrick and Keating (B&K) - page 12
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MHB Fourth or Lattice Isomorphism Theorem for Modules - clarification
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MHB Proof of Fourth or Lattice Isomorphism Theorem for Modules
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MHB Modules - Decomposibiity of abelian groups
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Graduate Trouble setting up to prove unique factorization
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MHB Is Matrix A Invertible Given (AB)C Equals the Identity Matrix?
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MHB System of linear equations, all possible outcomes
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MHB K^n as a K[T]-module - Example 2.1.2
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Graduate How Is the Killing Metric Normalized for Compact Simple Groups?
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Graduate Finding Lie-Algebra Invariants -- an Explicit Procedure?
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Graduate What is the connection between 2-forms, determinants, and cross products in R^3?
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MHB Indecomposable modules - example from Berrick and Keating
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MHB Find matrix representation with respect to the basis
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Graduate Ring Theory Problems: Unity vs. Non-Unity
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Undergrad Decompose a Recipe into Its Constituent Ingredients
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MHB Definition of Direct Product Using UMP - Including Infinite Case
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Undergrad Why Fields are Necessary for Linear Algebra
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MHB Using the given basis of a vector to prove other basis
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Graduate Understanding Adjoint Operators: A Helpful Explanation and Example
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Undergrad Are Slack Variables Causing Infeasible Points in Simplex Method?
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Graduate Converting an explicit series to a recursive form
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Undergrad Fast tridiagonal matrix algorithm
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MHB Infinite Direct Sums and Indexed Sets
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Graduate Inhomogeneous Linear System Solutions
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Graduate Unique solution to an arbitrary monotonic non-linear system
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MHB Can Complex Numbers Solve This Linear System?
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Undergrad Understanding Eigenspaces: Solving Exam Questions
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Undergrad How can linear equations be solved using matrices?
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MHB Universal Mapping Property of a Direct Sum - Knapp Pages 60-61
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MHB Isomorphism Between External and Internal Direct Sums - Knapp Proposition 2.30
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