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.
High School What Does Dimension Mean in Vector Spaces?
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MHB Showing That $(AB)x = A(Bx)$: A Clue!
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MHB Which is the velocity and the angle?
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MHB Dimension of $m \times n$ Matrices: Finding Basis
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MHB Does the triple product being zero guarantee coplanarity of vectors?
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High School What are the values in a vector?
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MHB What Are the Roots and Generators of the Polynomial $g$ in $\mathbb{F}_{16}$?
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MHB Verifying Subgroup Notation of $H(x_0)$ in $A(S)
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MHB The automorphic group is abelian
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MHB Proving the Normality of Inner Automorphism Group in Group Theory
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Undergrad Linear Transformation notation
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High School Application of Matrices and Determinants
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Graduate Confusion about eigenvalues of an operator
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MHB Which function do we define to show the homomorphism?
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MHB Does \( A_4 \) Have a Subgroup of Order 6?
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MHB Dimension & Subspace of $\mathbb{R}^3$
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MHB Subspace spanned by subsets of polynomials
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MHB How can the Wronskian be used to determine linear independence?
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Graduate Definition of an operator in a vector space
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Undergrad Insight/Intuition into rotations in R²
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MHB Every set of k+1 elements is dependent.
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MHB Why is theta restricted to [0,pi] in mathematics and physics?
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MHB Symmetric Polynomials s1,s2,s3
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MHB Yet Another Basic Question on Linear Transformations and Their Matrices
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MHB Distributing the Product of Functions over Composition of Functions
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MHB If a subset T of S is dependent, then S itself dependent
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Graduate Sextenions (6D hypercomplex numbers)
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MHB Find Equation of Plane Perpendicular to Line $l(t)$
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MHB Proving Span of $\mathbb{R}^2$ Using Sets of Vectors
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MHB Checking if an interval value satisfies an expression
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Undergrad Supremum = least upper bound, anything > supremum?
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MHB Isomorphism between $M$ and $S_3$: Finding the Corresponding Function
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MHB Proving That $G$ is Abelian When $G/Z$ is Cyclic
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MHB What is the center of $GL_n(\mathbb{R})$?
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MHB Understanding Aut(G) Isomorphism to Z2
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MHB Finding the Center of $S_n$: Understanding the Commutativity of Disjoint Cycles
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MHB Is $\text{Aut}(\mathbb{Z}_p)$ isomorphic to $\mathbb{Z}_{p-1}$?
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MHB Proving Evenness of m and r in σ ∈ Sn
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Graduate Quotient of group by a semidirect product of subgroups
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MHB Symmetric Polynomials Involving Discriminant Poly
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MHB How can we find a generator of the multiplicative group of a finite field?
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Undergrad What is the connection between cofactors, determinants, and matrix inverses?
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Graduate Can I bra through a Modulus in Quantum Mechanics?
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MHB How Does Burnside's Lemma Calculate the Number of Distinct Colored Cubes?
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MHB Proving Finite Groups: A Contradiction in Subgroups - Hello! (Wave)
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MHB How to Express a Force as a Sum of Parallel and Perpendicular Components?
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Undergrad How to find basis vectors for a+ ax^2+bx^4?
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MHB Are These Row Equivalent Matrices? Why Am I Getting Different Results?
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MHB What Do the Elements of $\mathbb{Z}_2 \times \mathbb{Z}$ Look Like?
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MHB Does This Cayley Table Accurately Represent the Dihedral Group \(D_6\)?
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MHB Matrices of Linear Transformations .... Example 2.6.4 - McInerney
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MHB (Very) Basic Questions on Linear Transformations and Their Matrices
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Graduate Am I Hallucinating? (confusion in geometric algebra)
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Graduate How Is the Abelianization of a Lie Group Defined?
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MHB Pinwheel Symmetry Formulas Exposed
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Graduate Definition of regular Lie group action
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MHB Quotient Groups & how to interpret notation?
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MHB Guarantee positiveness of an expression
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Graduate Approximate a spectrum from a series of measurements
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MHB Why Do Different Texts Present Bilinear Forms Differently?
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Graduate Is this complex vector orthogonal to itself?
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Graduate Polynomial splits over simple extension implies splitting field?
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Graduate Definition of a Cone: Does it Include Zero Vector?
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MHB Quartic polynomial has at least one real root
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MHB Vector Spaces .... Linear Dependence and Indepence .... Basic Proof Required
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MHB Help with functional analysis questions
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Graduate Langlands Programs: Learn What They Are & Why You're Curious
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Undergrad Interpretation: Solution to a set of Linear Equations
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Graduate Proof of Invertibility: Linear Map's Surjectivity and Injectivity Condition
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MHB Proof of Gρ(x)=ρGxρ−1 in Symmetric Groups
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Graduate Use of diagonal matrices in vibration analysis?
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MHB Solving the nature of intersection between 3 planes
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MHB Finding a Cayley Table for a Groupoid: an Example
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MHB Proving System of Equations for Algebra Challenge
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Graduate Lowest eigenstate of hopping matrix
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Graduate Elements of semigroup commuting with subgroup
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MHB Can All Linear Diophantine Equations Be Solved?
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Undergrad Can you rearrange vectors in a set? And another misc questn.
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Graduate Issue with behavior of ray-plane intersection algorithm
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Graduate Looking for a nice basis for the general linear group
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Undergrad What is the largest number of mutually obtuse vectors in Rn?
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Graduate Solution of a certain NxN matrix, when N->∞
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Graduate What shape does SO(3)/A5 describe and how can it be visualized?
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Graduate Is this proof of an ##\infty## norm valid?
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MHB Proving Existence of $N$ for $a^N=e$ in Finite Group $G$
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Graduate Am I understanding "supremum" correctly
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Graduate Find Lorentzian Scalar Product on 4-D Lie Algebra G
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MHB S3 Group Symmetry: $(xy)^2 \ne x^2y^2$ Example
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MHB Group R^× isomorphic to the group R?
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MHB Showing that a group is non-abelian
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MHB Prove function is a homomorphism
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Graduate Question about induced matrix norm
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MHB Vector or Parametric Form of the Equation of a Plane P
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Undergrad How to determine the smallest subspace?
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MHB Linear Applications: Electrical Networks
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MHB Prove Abelian Group: $(a \cdot b)^n = a^n \cdot b^n$
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MHB Two Versions of the Correspondence Theorem for Vector Spaces
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MHB Sum of Two Subspaces and lub - Roman, Chapter 1, page 39
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Graduate Understanding Equivariant Maps in Group Theory
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Graduate Understanding POVMs and Quantum Information in Corollary Proofs
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