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.
Matrix Rank: Meaning, Importance & What It Tells You
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Possibly silly linear algebra question
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Help with linear transformation problem with variables
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MHB Exact Sequences - Dummit and Foote Ch 10 - Proposition 29
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What Are the Automorphisms of Z[x]?
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MHB How do I Find the Vector Coordinates to Solve for Trihedral Angle?
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How to solve a system with more unknowns than equations?
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MHB Does (ab)^n Always Equal a^n*b^n in an Abelian Group?
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MHB Exact Sequences - Dummit and Foote Ch 10 - Proposition 28
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Yaw,Pitch and Roll Multiplication
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Demonstrating that a mapping is injective
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MHB How can I find the kernel of a homomorphism of finite groups?
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MHB Demonstrating that a mapping is injective
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Artin's lemma in Galois Theory: when is [E:F] < |G|?
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MHB How Do You List Elements of G/H in Z10 When H={α,β,δ}?
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Rate-of-strain tensor in cylindrical coords.
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MHB Understanding Finite Quotient Groups: G/H with G=Z6 and H=(0,3)
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MHB Exact Sequences - Lifting Homomorphisms - D&F Ch 10 - Theorem 28
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Exact Sequences - Lifting Homomorphisms - D&F Ch 10 - Theorem 28
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MHB Direct Products of Modules - Bland - Rings and Their Modules
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MHB Proof that Ha=Hb: Element y in Hb Proven True for Ha
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MHB Using dihedral group in Lagrange theorem
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(Apparently) simple question rearding module homomorphisms
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Do All Subspaces in Rn Have Orthonormal Bases?
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MHB Exact Sequences - extending or lifting homomorphisms
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MHB (Apparently) simple question rearding module homomorphisms
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MHB Split Sequences - D&F Ch 10 Section 10.5
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MHB Why can we show that an other polynomial is irreducible?
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MHB Polynomial Divisibility Problem: Proof & Corollary
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MHB Proving Lagrange Theorem for Finite Group G
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Prove that U_{m/n_1} (m) ,U_{m/n_k} (m) are normal subgroups
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Why is q=0 for Simple Roots in Lie Algebras?
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Direct Products of Modules - Bland - Proposition 2.1.1 and its proof
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MHB Direct Products of Modules - Bland - Proposition 2.1.1 and its proof
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MHB Basis of a vector space - apparently simple problem
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MHB Basic Question on Modules - Dummit and Foote Chapter 10
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Rotation and translation of basis to remove cross terms
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Direct Products of Modules - Bland - Rings and Their Modules
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What is Known About Zero-th Gaussian Periods of Type (N,r)?
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For every positive integer n there is a unique cyclic group of order n
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Unifying Different Definitions of Adjoint Map
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MHB Finding the projection of a vector.
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MHB How to Use Euclidean Division in $\mathbb{Z}_7$?
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MHB Why is sin(3pi/2) not equal to 1?
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Component is diagonal in the basis
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Does Preimage of Subgroup Under Homomorphism Form a Subgroup?
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Is it possible to solve for y using non-linear methods?
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MHB Proof of Exact Sequence Let $R$ & A Closed Set
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Embedding Group as a Normal Subgroup
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Are the Right and Left Cosets Equal in a Group's Cayley Table?
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How can I use linear programming to distribute S into two bins?
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Preliminary knowledge on tensor analysis
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Non-Symmetric Matrix: Real Eigenvalues Examples
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Confusion about basis vectors and matrix tensor
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Equality involving matrix exponentials / Lie group representations
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Is Tr(ABAB) Nonnegative for Symmetric Matrices A and B?
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Does Universal Algebra Have Applications in Physics?
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Interesting Subspaces of ##L^p## Spaces
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Matrix notation for Lorentz transformations
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MHB Glad I could help! Good luck with your studies.
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MHB Solving for D in a Confusing Matrix Equation | Invertible Matrices NxN
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General expanded form of (x+y+z)^k
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Understanding Skew Symmetric Matrices for Physics - A Helpful Guide
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MHB Greatest common divisor of polynomials
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MHB Looking for an Example of an Amusing Theorem in Linear Algebra.
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Inverse matrix notation question
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Position vector in curvilinear coordinates
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What is the practical application of the trace of a square matrix?
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Lie-algebra representation powers - plethysms
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Compute the Quotient: [Z+Z]/[2Z+2Z]
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Understanding Vector Transformations: Problem 1
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MHB How can you simplify generated ideals in a commutative unital ring?
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MHB Counting Cosets: Clarifying Right & Left Cosets
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Proof of the Lindemann-Weierstrass Theorem
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MHB Integral Ring Theory: Proving Integral Extension Property for Quotient Rings
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Rotation of Gridded Spherical Coordinates to the Same Grid
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Proof of the nontrivial expression
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What are Eigenvectors and Eigenvalues in Relation to Matrices?
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MHB Are \( x-a \) and \( x-b \) Co-primes?
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Where do the coefficients in this vector equation come from?
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Understanding the Relation Between Determinant and Trace in Physics Texts
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MHB Why do we conclude that p|exactly one of b0,c0?
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Showing that V is a direct sum of two subspaces
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Matrix multiplication - is this plausible?
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Can any vector be in orthonormal basis?
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How Does Cramer's Rule Relate to Geometry?
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How to prove if a recursive system is linear?
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MHB Are all subrings and units correctly identified in algebraic structures?
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Matrix Index Inversion: Clarification Needed
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Identifying Largest Submatrices in a 0/1 Matrix?
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Generalised eigenspace contains the eigenspace?
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MHB Find the coefficient of x^{21} without calculating the product
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MHB Find all the zero divisors in a ring
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MHB Finding the Units of the Ring $R=\mathbb{Z}[w]$
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MHB Do I Have to Show All Axioms to Prove a Set is a Ring?
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How to Efficiently Solve a Tridiagonal Matrix with Fringes?
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MHB Understanding the Linear Independence of Columns in a 3x5 Matrix
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MHB P divides all the coefficients of the terms with degree <8
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What is the General Expression for the Product of Two Matrix Exponentials?
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Solving Clifford Algebra Equation - Need Help!
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