Linear and Abstract Algebra Forum

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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.
Graduate Given S, T, prove that ST and TS have the same eigenvalues.
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Graduate Using Quadratic formula in other fields
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Undergrad How to find eigenvalues/eigenvectors
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Undergrad Can matrices be used to solve systems with different degree variables?
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Graduate Is there a proof for the new Mersenne numbers conjecture?
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Graduate Regarding Diagonalization of Matrix by Spectral Theorem
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Undergrad Subspaces of R2 and R3: Understanding Dimensions of Real Vector Spaces
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Graduate Conjecture re form x^2 + Mxy + y^2
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High School Question about Scalar Product of Vectors
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Graduate Normalizer & normal subgroup related
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High School : simple problem 3x = 1 (mod 16), find all possible values of x mod 16
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Graduate Parallel discrete logs (continues: modular arithmetic)
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Undergrad What is the use of the convolution theorem in multiplying large numbers?
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Graduate How to Prove the Eigenvalue Property of CrA(x)?
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Graduate Understanding Composition of Point Symmetry Generators in Lie Algebras
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Graduate Why is d(x^TCx) equal to x^T(C+C^T)dx?
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Graduate Is Symmetry Crucial in Understanding Group Theory?
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High School Simple problem 3x = 1 (mod 16), find all possible values of x mod 16
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Graduate Understanding the Definition of the Adjoint Operator in Linear Algebra
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Undergrad Solving 2^k ≡ n mod p with Modular Arithmetic
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Graduate Defining +0 and -0 in the Integer Number Set: A Question of Limit Approaches
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Graduate Is 0 Considered a Prime Element in an Integral Domain?
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Graduate How Does the Cross Product Work in Geometric Algebra?
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Graduate Generation of isomorphic fields by separate algebraic elements
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Graduate Equivalence of Irreducibility Tests for Polynomials Under Variable Substitution
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High School Number Theory: An Overview for Beginners
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Help with understanding of relations of numbers and members
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Graduate Matrix Binomials: Struggling to Interpret Question
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Graduate Proving Reversibility of A with u & v of Size n*1
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Graduate How can we accurately compute the matrix exponential?
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Graduate Conversion from Cartesian to toroidal coordinates
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Undergrad Showing a mapping is onto and/or one to one
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Graduate Physics and Mathematics - what are the unsolved problems?
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Undergrad Vectors Spanned & Linear Independence
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Graduate Maximal ideal question, + invertibility
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Graduate Conjugate and Inverse Quaternions
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Undergrad How do you determine the intersection of two vector subspaces?
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Graduate Graded Commutative Algebra: A Comprehensive Reference
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Graduate Is Idempotent Equivalence in Rings Transitive?
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Undergrad Proving Singular Matrix A Has Nonzero Matrix B: Linear Algebra Problem
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High School What is Number Theory? Unraveling the Mystery
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Graduate Good Algebra Textbook: Basic to Graduate Level
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Graduate Asymptotic expansion for Mertens function
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Undergrad Confused about unit vector equivalence
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Undergrad Determinant Expansions: Intuitive Understanding & Proofs
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Undergrad Where Can I Find a Quick Start Guide for Learning Category Theory?
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Graduate Help With Proving a is Zero Divisor Mod n iff gcd(a,n)>1
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Undergrad Making a Set a Basis: Is V Spanned?
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Undergrad What is the value of ||\vec{x}||How to Approach a Vector Projection Problem?
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Undergrad Infinity subtracted from infinity is undefined.
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Graduate Linear Operators: False for Non-Finite Dimensional Vector Spaces
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Graduate Elements of SO(3): Listing All Matrices
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Undergrad What is the Solution to Finding a Set of n+1 Integers from 2n?
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Graduate Irreducibility in multiple dimensions
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Graduate Proving N(H) is a Subgroup of G to Normalizers in Group Theory
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Graduate Needed: Help with proving commutitivity
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Graduate Q1: Does A and its transpose have the same eigenspace?
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Graduate Generating Rings with Ideals: The Possibilities and Implications
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Undergrad Why Is Matrix Multiplication Defined the Way It Is?
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Graduate Proving a Dimensional Inequality for Null Spaces of Linear Transformations
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Undergrad How Can We Represent and Sum the Rows of This Manipulated Pascal's Triangle?
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Graduate Conjecture about Dirichlet series.
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Graduate Proof of Infinite Cyclic Group Isomorphism to Z
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Graduate How Do Quotient Spaces Relate to Periodic Boundary Conditions in Mathematics?
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Undergrad Can isomorophisms be really random?
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High School Check If Vector is Constant: Explanation & Tutorial
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Graduate Fast Test for Semiprimes: Deterministic or Probabilistic?
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Graduate General Form of 3x3 unitary matrix
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Undergrad Can linear least squares be used for inverse function approximation?
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Graduate What is the correct method for transforming a matrix to a new basis?
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Undergrad Can I Use Linear Algebra to Prove the Equation det(AB) = det(A) det(B)?
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Undergrad Distributive Properties of the Determinate
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Undergrad Why Does a Subset of a Vector Space Need the Zero Vector to Be a Subspace?
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Undergrad Linear Algebra in Physical Science and Engineering: Theory and Applications
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Graduate Proving Vector Space of F[x]/(g(x)) with Degree n
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Graduate Is 1 considered the zero vector in this scenario?
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Undergrad Solving Linear Algebra Problem: Eliminating p_2 with Diagonal D
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High School Why Do Solutions Sometimes Differ from Absolute Values?
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Undergrad Linear Algebra: need suggestions for learning
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Graduate Is the Real Number Set Countable with a Special Function?
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High School Zero product property for integers
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Undergrad MIT OpenCourseWare Linear Algebra
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Graduate What is the role of the Axiom of Choice in algebraic structures?
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Graduate Constructing a Stiffness Matrix for Research on Rat Scoliosis
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Graduate Inner products, operators, equality
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Graduate Proving 0v=0 using only the 10 Axioms
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Graduate A quesion about Field of quotients
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Graduate Irreducible reps of maximal tori
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Undergrad 196-Algorithm (palindromic numbers)
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Undergrad Understanding Coset Representation and its Role in Group Theory
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Graduate Problem Dealing with Digit Cycles
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Graduate A group G has exactly 8 elements or order 3
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Undergrad 2 Questions, regarding closure
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Graduate Can 2z^n(z^n + x^n + y^n) Ever Be a Perfect Square for Prime n Greater Than 2?
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Graduate Conjecture on triangular numbers T(n)
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Graduate Group Theory-solution to polynomial equations
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Undergrad Solving Higher Order Polynomial: ax + x^3 - x^5 = 0
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Graduate What are the v_j vectors in Cahn's representation of the Lie algebra of SO(3)?
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Undergrad Can someone explain Euler angles?
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Undergrad Help with Proof: GCD(a,bk) = GCD(a,k)
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