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
Graduate What are some real-world applications of cyclic groups and Galois fields?
- jimmycricket
- · Replies 7 ·
Graduate Struggling to understand a field theorm's corollary
- PsychonautQQ
- · Replies 3 ·
Graduate Every field contains a copy of Z_p
- PsychonautQQ
- · Replies 5 ·
Matrices Show that Tr(A + B) = Tr(A) + Tr(B).
- MaXiiMo
- · Replies 3 ·
Find a Basis for U with $\text{rref}(A)$
- Dethrone
- · Replies 10 ·
Graduate Trouble understanding simple Galois Theory example
- PsychonautQQ
- · Replies 1 ·
A Basic Question Regarding the Universal Property of the Tensor Product.
- caffeinemachine
- · Replies 2 ·
Graduate Alternate expression for definition of an Ideal?
- PsychonautQQ
- · Replies 4 ·
Undergrad Structure of a Matrix With Empty Null Space
- Paul Shredder
- · Replies 3 ·
Graduate Problems understanding proof of Cauchy theorem
- PsychonautQQ
- · Replies 6 ·
Undergrad Zero eigenvalues or eigenvectors
- nomadreid
- · Replies 6 ·
Graduate Need help understanding splitting fields
- PsychonautQQ
- · Replies 4 ·
Undergrad Can anyone give an intuitive proof of the theorem on polynomial factorization?
- Shahed al mamun
- · Replies 1 ·
Reflection Matrices: Find Components of R
- Ciaran
- · Replies 4 ·
Graduate Scalar triple product and abstract vector space
- PcumP_Ravenclaw
- · Replies 4 ·
Convert infinite solution to vector form
- ibwev
- · Replies 6 ·
What Are the Basic Properties of This Lie Algebra?
- topsquark
- · Replies 1 ·
Undergrad Simple explanation of group generators
- resurgance2001
- · Replies 9 ·
SU(2) and elementary properites of Lie Algebras
- topsquark
- · Replies 12 ·
Issue 2 - Tapp - Characterizations of the Orthogonal Groups
- Math Amateur
- · Replies 5 ·
Characterizations of the Orthogonal Groups _ Tapp, Ch. 3, Section 2
- Math Amateur
- · Replies 3 ·
Graduate Solving for P_x(X) given P_y(Y) and P_(x+y)(X+Y)
- Boorglar
- · Replies 5 ·
High School Can you solve this system of simultaneous equations?
- physior
- · Replies 7 ·
Graduate Algorithm to find square root of a quadratic residue mod p
- tjkubo
- · Replies 2 ·
Rotations, Complex Matrices and Real Matrices - Proof of Tapp, Proposition 2.2
- Math Amateur
- · Replies 10 ·
Rotations, Complex Matrices and Real Matrices
- Math Amateur
- · Replies 7 ·
Graduate A question about derived functors
- Jim Kata
- · Replies 4 ·
Undergrad Applying rules to simplify a 3 x 3 determinant
- PcumP_Ravenclaw
- · Replies 1 ·
Undergrad I need to transpose for the value of Q
- Rodo
- · Replies 3 ·
Graduate Algebraic Closure: Finite Fields & Equivalent Statements
- PsychonautQQ
- · Replies 3 ·
Graduate Have you done PA=LU factorization?
- LongApple
- · Replies 10 ·
Graduate Components of adjoint representations
- synoe
- · Replies 1 ·
Graduate No cycles in permutation N how to calculate sgn(N^2)?
- ilyas.h
- · Replies 2 ·
Does Property (2) Imply Property (1) for Unit Quaternions?
- Math Amateur
- · Replies 2 ·
Is a Shifted Solution Still Valid?
- Yankel
- · Replies 10 ·
Graduate Definition of unconnected subgroups
- PsychonautQQ
- · Replies 6 ·
Undergrad How Do You Calculate the Square of a Permutation Matrix?
- ilyas.h
- · Replies 6 ·
What is the purpose of computing the transpose of a matrix?
- shamieh
- · Replies 2 ·
Undergrad Confused about vectors and transformations (linear)
- GiuseppeR7
- · Replies 2 ·
Graduate Maximal ideal not containing specific expression
- coquelicot
- · Replies 2 ·
Graduate Euclidean space: dot product and orthonormal basis
- rkaminski
- · Replies 8 ·
Graduate Not understanding the isomorphism R x R = C
- metapuff
- · Replies 3 ·
Order of Operations for Matrices in Scientific Computing
- shamieh
- · Replies 1 ·
Parametric equations and augmented coefficient matrices
- boriskov
- · Replies 1 ·
Undergrad Row/column operation on matrices and determinants
- Raghav Gupta
- · Replies 11 ·
Graduate Adjoint and inverse of product of operators
- ellilu11
- · Replies 8 ·
Graduate Understanding Aut(Aut(Aut(C_73))) in Group Theory
- jimmycricket
- · Replies 2 ·
Graduate How can the Sherman-Morrison formula simplify matrix inversion?
- nikozm
- · Replies 1 ·
Linearly Independent: Why ${}\left\{X+Y, Y+Z, Z+W, W+X\right\}$ Isn't
- Dethrone
- · Replies 5 ·
Graduate When is integral closure generated by one element
- coquelicot
- · Replies 4 ·
Understanding a problem in ring theory
- kalish1
- · Replies 5 ·
Graduate Unique factorization over fields/rings
- PsychonautQQ
- · Replies 2 ·
Undergrad Image of a Matrix and symmetric matrix
- Payam30
- · Replies 3 ·
Calculation of the commutator of the hamiltonian and position
- Fantini
- · Replies 5 ·
Graduate Riemann's zeta function fractal because of Voronin?
- nomadreid
- · Replies 2 ·
Graduate Vector multiply that is NOT dot or cross?
- ognik
- · Replies 6 ·
Undergrad Question on solving linear recurrence relations
- japplepie
- · Replies 1 ·
Graduate Why there's no L^2[-inf,inf] space?
- jorgdv
- · Replies 2 ·
Undergrad How can I solve a system of equations with two unknowns?
- Quadrat
- · Replies 8 ·
Graduate Which is the space of mappings from L^2 to itself?
- jorgdv
- · Replies 2 ·
Undergrad How does L from LU give us column space?
- LongApple
- · Replies 1 ·
Lower Central Series: Meaning of Gamma of G
- Pratibha
- · Replies 1 ·
Graduate Question on group theory: simplest math construction
- Abolaban
- · Replies 1 ·
Graduate Complex Representations: Real vs. Complex Lie Algebras
- Lapidus
- · Replies 3 ·
Graduate Linearity in the Vector triple product
- PcumP_Ravenclaw
- · Replies 6 ·
Simple Grammar Problem: Is "a" or "the" Ideal in Lie Algebra?
- topsquark
- · Replies 3 ·
Undergrad Intuition & use of M*M^T product of matrix & its transpose?
- NotASmurf
- · Replies 6 ·
Range and Image of a Transformation
- bwpbruce
- · Replies 6 ·
Graduate Basic transcendental field extension question
- PsychonautQQ
- · Replies 1 ·
Graduate Understanding Scalar Triple Product (STP)
- PcumP_Ravenclaw
- · Replies 4 ·
Violation of Linear Transformation?
- bwpbruce
- · Replies 6 ·
Graduate Understanding Basis Change with Hamiltonian Matrices
- aaaa202
- · Replies 3 ·
Proof of Conjugate Cycles Property of Permutations
- Kiwi1
- · Replies 1 ·
Ideals of formal power series ring
- Anonymous2
- · Replies 1 ·
Transformation of a Parallelogram
- bwpbruce
- · Replies 3 ·
Linear Transformation of a Plane
- bwpbruce
- · Replies 2 ·
Sketch of the Reflection Transformation of a Parallelogram
- bwpbruce
- · Replies 2 ·
Undergrad How Do You Simplify This Vector Expression?
- izchief360
- · Replies 5 ·
Graduate Calculating angle of circle to produce given ellipse
- HKragh
- · Replies 6 ·
Show that a Parametric Equation Maps To Another Line By Linear Transformation.
- bwpbruce
- · Replies 3 ·
Undergrad Prove to myself that rotation is a linear transformation?
- davidbenari
- · Replies 4 ·
Graduate Do Gramian Matrices Have Only One Non-Zero Eigenvalue?
- I_am_learning
- · Replies 5 ·
Graduate Help finding a topic in Number Theory
- MostlyHarmless
- · Replies 5 ·
Undergrad Determine if all vectors of form (a,0,0) are subspace of R3
- 7sqr
- · Replies 10 ·
Undergrad Gaussian elimination: Proof of correctness
- Bipolarity
- · Replies 13 ·
Is $f(x) = mx + b$ a Linear Transformation?
- bwpbruce
- · Replies 11 ·
Graduate Understanding the fundamental theorem of algebra
- PcumP_Ravenclaw
- · Replies 11 ·
Graduate Why is the core of a subgroup contained in the subgroup?
- PsychonautQQ
- · Replies 6 ·
Graduate Properties, General Results on of Aut(G) ?
- WWGD
- · Replies 2 ·
Solving (A+B)^-1: Is A^-1+ B^-1 the Answer?
- roscany
- · Replies 4 ·
How Do You Prove Two Spans Are Equal?
- Dethrone
- · Replies 2 ·
Graduate Does an operation have to be closed?
- nomadreid
- · Replies 17 ·
Graduate Eigenvalues/vectors of Hermitian and corresponding unitary
- nomadreid
- · Replies 4 ·
Extending Vectors to a Basis of R^4: Why Notation Matters
- Yankel
- · Replies 1 ·
Undergrad Graphing Functions in n Dimensions, Parametric Equations
- TheDemx27
- · Replies 1 ·
Is \( U \) a Subspace of \( F[0,1] \)?
- Dethrone
- · Replies 6 ·
Graduate Why do the conjugate classes of a group partition the group?
- PsychonautQQ
- · Replies 1 ·
Undergrad Rotation matrix multiplied by matrix of column vectors?
- aaddcc
- · Replies 5 ·
Graduate Why Is the Index Shifted in Laplacian Eigenvalues?
- member 428835
- · Replies 5 ·
Is My Matrix Solution Correct?
- pHlawless
- · Replies 4 ·