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.
MHB Help with $(iii)$ of Math Problem on MHB
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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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