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.
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Graduate Green's Function - modified operator
- RightFresh
- · Replies 9 ·
Undergrad Matrices and systems of equations
- Avatrin
- · Replies 2 ·
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 Why does the splitting field of x^4 - 6x^2 - 7 over Q involve √2?
- PsychonautQQ
- · Replies 4 ·
Undergrad Intuitive proof that polynomials factor into linear and irreducible quadratic factors
- Shahed al mamun
- · Replies 1 ·
Finding the matrix R for reflection across a line
- 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 Are derived functors of adjoint functors also adjoint?
- 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 Why are these two characterizations of algebraic closure for finite fields equivalent?
- 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 Are column vectors always coordinates with respect to a basis?
- GiuseppeR7
- · Replies 2 ·
Graduate Maximal ideal not containing specific expression
- coquelicot
- · Replies 2 ·
Graduate Defining dot product and orthonormal basis consistently in Euclidean space
- rkaminski
- · Replies 8 ·
Graduate Why isomorphism R × R ≅ C doesn't preserve ideal structure
- 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 Why multiply a matrix by 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 ·
Reflection through the x₂ axis: linear transformation properties
- 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 ·
Linear transformation maps a line to a line or point
- 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 Number theory paper topics for 10-15 pages
- MostlyHarmless
- · Replies 5 ·
Undergrad Determine if all vectors of form (a,0,0) are subspace of R3
- 7sqr
- · Replies 10 ·
Undergrad Proof that Gaussian elimination produces row echelon form
- Bipolarity
- · Replies 13 ·
Is $f(x) = mx + b$ a Linear Transformation?
- bwpbruce
- · Replies 11 ·
Graduate Proof that nth-degree polynomial has n roots by induction
- 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 ·