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.
Cauchy Schwarz equality implies parallel
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MHB Is There a Better Way to Approach Vector Identities?
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What do you call a_ji in relation to a_ij
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MHB Solving 2x2 Matrix Projection Problem: Strang's Approach
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MHB Solve Simultaneous Equations: No/1/Inf Solns?
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MHB How Does the Correspondence Theorem Prove Maximal Submodules and Simplicity?
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MHB I want to visualise this vector expression
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MHB How does using cross product to find shortest distance work?
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MHB Correspondence Theorem for Modules - Rotman, Section 6.1
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MHB Corollary to Correspondence Theorem for Modules
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Rotman's Remarks on Modules in Context of Chain Conditions
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When is the Cauchy-Schwartz inequality as large as possible?
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Matrix with repeated eigenvalues is diagonalizable....?
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Estimating singular values from QR decomposition
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Connection between subspace, span, and basis?
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Looking for insight into what the Determinant means....
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MHB Unlock Role of Correspondence Thm for Groups in Analysing Composition Series
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High Order Polynomials: Questions & Answers
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MHB Prove the polynomial f(x)=x^2-q is irreducible in F_p[x]?
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MHB Check another visualise vector expression
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MHB Why Does $\vec{n}.\vec{r}$ Equal $d$ for a Parallel Line?
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MHB What is Aluffi's notation for composition series in Algebra: Chapter 0?
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Outer products & positive (semi-) definiteness
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Eigenvector of Pauli Matrix (z-component of Pauli matrix)
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MHB Jordan-Holder Theorem for Groups .... Aluffi, Theorem 3.2
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Convert ECI to ECEF: A Step-By-Step Guide
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Understanding proof for theorem about dimension of kernel
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X0 value for Newton's forward interpolation formula
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Cyclic Quotient Group: Is My Reasoning Sound?
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MHB Consequence of Hilberts Nullstellensatz - Dummit & Foote, Section 15.2
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When Should You Use the Law of Cosines in Electrodynamics?
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MHB What could we change so that EXP(C) is a ring?
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MHB Paul E Bland's "Direct Product of Modules" Definition - Category-Oriented
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Polynomial Degree n Basis: 1,x,x^2...x^n
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Does this kind of space have a name?
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MHB Understanding Direct Products of Vector Spaces: Cooperstein's Example 1.17
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What units will this equation have?
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Dimension of the span of a set of vectors
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MHB Linear Algebra: General Solution, Stability & Diagonal Transforms
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MHB Proposition 3.1.2 in B&K: Help Needed on Exact Sequences/Noetherian Rings
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MHB Corollary 3.1.3 - Berrick and Keating - Noetherian Modules
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MHB Group Theory: Finite Group Has Prime Order Element
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Can the basis minor of a matrix be the matrix itself?
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MHB Affine Algebraic Sets - Properties of the map I - Dummit and Foote, page 661
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MHB Help Needed: Analzying Berrick & Keating's Prop. 3.1.2 on Noetherian Rings
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MHB Exact Sequences and Noetherian Rings - Proposition 3.1.2 - Berrick and Keating
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Finding crossing regions between two quadractics
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Finding the ideals of an algebra
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What is the Tensor Product of Vectors and How Does It Differ Across Contexts?
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Row and null complements of x; need clarity....
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MHB Matrix Algebra 2.0 Help: Solving Questions with Cosine Laws
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MHB Field Extensions - Discussion of Dummit and Foote - page 512
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Dimension of all 2x2 symmetric matrices?
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MHB Find All Subgroups of U(14) in $\mathbb{Z}_{14}$
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MHB Solving Linear Systems with a Variable: How to Handle Unknown Constants?
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MHB Need Help with University Question? Let's Discuss!
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Parametrize the solution set of this one-equation system.
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Solving sturm-liouville equations
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MHB Solving Coefficant Matrices with Legendre Polynomials
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MHB Radicals of Ideal: Get Help Understanding D&F Prop. 11
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Abstract Algebra: Beyond and Higher?
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MHB Checking Field Axioms for $G = F \times F$
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MHB Check sturm-liouville orthogonality problem
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Matrix Elements as images of basis vectors
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What subspace of 3x3 matrices is spanned by rank 1 matrices
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Isn't chemistry just applied algebra/pre-calculus?
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What are the limitations and capabilities of pseudo inverses?
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Matrix is Invertible: is this notation ok?
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The extremes of an nth dimension linear equation
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MHB Proving Self-Adjoint ODE for Legendre Polynomials
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MHB Evaluating Orthogonal Integral for Legendre Equations
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MHB Conjugate Bra Ket Properties for Proving the Schwarz Inequality
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MHB Sturn-Liouville equation subtraction
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How to find composition series of Z_n^* of length k?
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MHB What Am I Getting Wrong About Matrices and Operators?
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MHB Proving Linear Independence of Eigenfunctions of a Hermitian Operator
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Column space and nullspace relationship?
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Is this the correct way to compute the row echelon form?
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MHB How can we show that all the solutions are given by X_m(a), Y_m(a) ?
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Abstract Algebra: Automorphisms
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MHB Can Different Bases Change the Classification of Lie Algebras?
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MHB Re-configurable Battery Network Modeling
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English translated German Linear Algebra book
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MHB To what is X_{-m}+α(a)Y_{-m} equal?
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How to find group types for a particular order?
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MHB Determinant always equal to zero?
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MHB Is <L^2> always greater than or equal to 0 for a Hermitian operator?
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Help: All subspaces of 2x2 diagonal matrices
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Norm indueced by a matrix with eigenvalues bigger than 1
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MHB LU Factorization - Solve with Carter Barker
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Onto equivalent to one-to-one in linear transformations
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MHB Radicals and Radical Ideals, Dummit and Foote Proposition 11, Section 15.2
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Converse of Lagrange's Theorem for groups
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MHB Terminology - Hermitian, adjoint ....
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Transform that maps points from any quad to an reactangle
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MHB Divisors of Zero in Rings: A[x] and the Impossibility in Polynomial Rings
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What exactly are matrices and determinants?
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Complex number and split complex number
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Undergrad Can This Formula Identify All Prime Numbers?
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MHB How is the Map $\tilde{\varphi}$ Well-Defined in Algebraic Geometry?
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