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
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 ·
Graduate Is the numerator in an induced matrix norm a vector norm?
- charlies1902
- · Replies 14 ·