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.
Threads
Linear Subspaces: Properties and Examples
- Guest2
- · Replies 2 ·
Field Extensions for polynomials
- mathjam0990
- · Replies 3 ·
Why does dual basis e*_1 depend on the entire basis?
- Math Amateur
- · Replies 2 ·
How Are Coefficients of a Vector Linear Functions of the Vector?
- Math Amateur
- · Replies 2 ·
High School How can you factorize polynomials with fourth degree terms?
- gede
- · Replies 12 ·
Finding equation normal to a plane and certain point
- brunette15
- · Replies 2 ·
How do you change the basis of vectors in $\mathbb{R}^3$?
- Guest2
- · Replies 2 ·
How Does E Relate to Q[x]/(x²+x+1) in Complex Algebra?
- mathjam0990
- · Replies 1 ·
Finding the dimension of a solution space for a homogeneous system
- Guest2
- · Replies 3 ·
High School What Does Dimension Mean in Vector Spaces?
- toforfiltum
- · Replies 6 ·
Showing That $(AB)x = A(Bx)$: A Clue!
- evinda
- · Replies 3 ·
Which is the velocity and the angle?
- mathmari
- · Replies 2 ·
Dimension of $m \times n$ Matrices: Finding Basis
- Guest2
- · Replies 2 ·
Does the triple product being zero guarantee coplanarity of vectors?
- evinda
- · Replies 3 ·
High School What are the values in a vector?
- The Subject
- · Replies 7 ·
What Are the Roots and Generators of the Polynomial $g$ in $\mathbb{F}_{16}$?
- evinda
- · Replies 11 ·
Verifying Subgroup Notation of $H(x_0)$ in $A(S)
- Guest2
- · Replies 7 ·
The automorphic group is abelian
- mathmari
- · Replies 14 ·
Proving the Normality of Inner Automorphism Group in Group Theory
- mathmari
- · Replies 6 ·
Undergrad Linear Transformation notation
- The Subject
- · Replies 4 ·
High School Application of Matrices and Determinants
- Obliv
- · Replies 6 ·
Graduate Confusion about eigenvalues of an operator
- maNoFchangE
- · Replies 4 ·
Which function do we define to show the homomorphism?
- mathmari
- · Replies 13 ·
Does \( A_4 \) Have a Subgroup of Order 6?
- mathmari
- · Replies 15 ·
Finding dimensions of subspaces of ℝ³ defined by linear constraints
- Guest2
- · Replies 8 ·
Subspace spanned by subsets of polynomials
- Guest2
- · Replies 3 ·
How can the Wronskian be used to determine linear independence?
- Guest2
- · Replies 2 ·
Graduate Definition of an operator in a vector space
- maNoFchangE
- · Replies 8 ·
Undergrad Insight/Intuition into rotations in R²
- STENDEC
- · Replies 3 ·
Every set of k+1 elements is dependent.
- Guest2
- · Replies 2 ·
Why is theta restricted to [0,pi] in mathematics and physics?
- evinda
- · Replies 8 ·
Symmetric Polynomials s1,s2,s3
- mathjam0990
- · Replies 2 ·
Coordinates of F(u₁) relative to standard basis in Example 6.1
- Math Amateur
- · Replies 5 ·
Distributing the Product of Functions over Composition of Functions
- Math Amateur
- · Replies 6 ·
If a subset T of S is dependent, then S itself dependent
- Guest2
- · Replies 3 ·
Graduate Sextenions (6D hypercomplex numbers)
- EinsteinKreuz
- · Replies 10 ·
Find Equation of Plane Perpendicular to Line $l(t)$
- evinda
- · Replies 1 ·
Proving Span of $\mathbb{R}^2$ Using Sets of Vectors
- Guest2
- · Replies 1 ·
Checking if an interval value satisfies an expression
- Siron
- · Replies 1 ·
Undergrad Supremum = least upper bound, anything > supremum?
- pyroknife
- · Replies 8 ·
How do you define the isomorphism from M to S_3?
- mathmari
- · Replies 22 ·
Proving That $G$ is Abelian When $G/Z$ is Cyclic
- mathmari
- · Replies 6 ·
What is the center of $GL_n(\mathbb{R})$?
- evinda
- · Replies 7 ·
Understanding Aut(G) Isomorphism to Z2
- mathmari
- · Replies 34 ·
Finding the center of S_n using disjoint cycle representation
- evinda
- · Replies 8 ·
Is $\text{Aut}(\mathbb{Z}_p)$ isomorphic to $\mathbb{Z}_{p-1}$?
- mathmari
- · Replies 15 ·
Proving Evenness of m and r in σ ∈ Sn
- namzay300
- · Replies 3 ·
Graduate Quotient of group by a semidirect product of subgroups
- mnb96
- · Replies 19 ·
Symmetric Polynomials Involving Discriminant Poly
- mathjam0990
- · Replies 2 ·
How can we find a generator of the multiplicative group of a finite field?
- evinda
- · Replies 14 ·
Undergrad How do cofactors, determinants, and the adjugate matrix relate in finding inverses?
- gfd43tg
- · Replies 8 ·
Graduate Can I bra through a Modulus in Quantum Mechanics?
- kq6up
- · Replies 2 ·
How Does Burnside's Lemma Calculate the Number of Distinct Colored Cubes?
- mathjam0990
- · Replies 1 ·
Does a group with finitely many subgroups have to be finite?
- evinda
- · Replies 12 ·
How to Express a Force as a Sum of Parallel and Perpendicular Components?
- evinda
- · Replies 1 ·
Undergrad How to find basis vectors for a+ ax^2+bx^4?
- DhineshKumar
- · Replies 3 ·
Why are my and my book's reduced row echelon forms different?
- Pull and Twist
- · Replies 1 ·
What Do the Elements of $\mathbb{Z}_2 \times \mathbb{Z}$ Look Like?
- mathmari
- · Replies 3 ·
Does This Cayley Table Accurately Represent the Dihedral Group \(D_6\)?
- Guest2
- · Replies 9 ·
Finding T(e1), T(e2), T(e3) in example 2.6.4 of McInerney
- Math Amateur
- · Replies 12 ·
(Very) Basic Questions on Linear Transformations and Their Matrices
- Math Amateur
- · Replies 2 ·
Graduate Why does abcdabcd equal -1 in geometric algebra?
- Hornbein
- · Replies 2 ·
Graduate How Is the Abelianization of a Lie Group Defined?
- mnb96
- · Replies 3 ·
Pinwheel Symmetry Formulas Exposed
- mathjam0990
- · Replies 5 ·
Graduate Definition of regular Lie group action
- mnb96
- · Replies 15 ·
Quotient Groups & how to interpret notation?
- mathjam0990
- · Replies 2 ·
Guarantee positiveness of an expression
- Siron
- · Replies 3 ·
Graduate Approximate a spectrum from a series of measurements
- maka89
- · Replies 3 ·
Why Do Different Texts Present Bilinear Forms Differently?
- Math Amateur
- · Replies 2 ·
Graduate Why is the inner product of (i,0,1) with itself zero?
- Steve Turchin
- · Replies 1 ·
Graduate Polynomial splits over simple extension implies splitting field?
- MostlyHarmless
- · Replies 5 ·
Graduate Definition of a Cone: Does it Include Zero Vector?
- Bashyboy
- · Replies 3 ·
Quartic polynomial has at least one real root
- Siron
- · Replies 2 ·
Proof of linear independence theorem in McInerney's differential geometry text
- Math Amateur
- · Replies 1 ·
Measure theory, integral equations, and Hilbert spaces
- simpleton1
- · Replies 9 ·
Graduate What are the Langlands programs?
- NoodleDurh
- · Replies 4 ·
Undergrad Interpretation: Solution to a set of Linear Equations
- chaoseverlasting
- · Replies 2 ·
Graduate Proof of Invertibility: Linear Map's Surjectivity and Injectivity Condition
- maNoFchangE
- · Replies 5 ·
Proof of Gρ(x)=ρGxρ−1 in Symmetric Groups
- mathjam0990
- · Replies 2 ·
Graduate Use of diagonal matrices in vibration analysis?
- theone
- · Replies 5 ·
Solving the nature of intersection between 3 planes
- sawdee
- · Replies 6 ·
Finding a Cayley Table for a Groupoid: an Example
- mathmari
- · Replies 3 ·
Proving System of Equations for Algebra Challenge
- anemone
- · Replies 8 ·
Graduate Lowest eigenstate of hopping matrix
- Fightfish
- · Replies 5 ·
Graduate Elements of semigroup commuting with subgroup
- mnb96
- · Replies 4 ·
Can All Linear Diophantine Equations Be Solved?
- Guest2
- · Replies 4 ·
Undergrad Does rearranging vectors in a set affect linear dependence?
- CookieSalesman
- · Replies 7 ·
Graduate Issue with behavior of ray-plane intersection algorithm
- STENDEC
- · Replies 7 ·
Graduate Looking for a nice basis for the general linear group
- Strilanc
- · Replies 3 ·
Undergrad What is the largest number of mutually obtuse vectors in Rn?
- RandomGuy1
- · Replies 4 ·
Graduate Solution of a certain NxN matrix, when N->∞
- onkel_tuca
- · Replies 2 ·
Graduate What shape does SO(3)/A5 describe and how can it be visualized?
- nateHI
- · Replies 1 ·
Graduate Is this proof of an ##\infty## norm valid?
- pyroknife
- · Replies 19 ·
Proving Existence of $N$ for $a^N=e$ in Finite Group $G$
- Guest2
- · Replies 7 ·
Graduate Is the supremum of x in x ≤ y equal to y?
- pyroknife
- · Replies 9 ·
Graduate Find Lorentzian Scalar Product on 4-D Lie Algebra G
- kroni
- · Replies 1 ·
S3 Group Symmetry: $(xy)^2 \ne x^2y^2$ Example
- Guest2
- · Replies 1 ·
Group R^× isomorphic to the group R?
- mathjam0990
- · Replies 5 ·
Showing that a group is non-abelian
- Guest2
- · Replies 7 ·
Prove function is a homomorphism
- mathjam0990
- · Replies 2 ·