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.
Find n such that the group of the n-th roots of unity has exactly 6 generators
  • AutGuy98
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Prove that the 12-th roots of unity in C form a cyclic group
  • AutGuy98
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Prove Lagrange’s Theorem for left cosets
  • AutGuy98
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3
Undergrad Transforming Vectors and Tensors
  • fog37
  • · Replies 8 ·
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8
Undergrad Showing direct sum of subspaces equals vector space
  • schniefen
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Graduate Diffusion equation and a system of equations with reciprocal unknowns?
  • Hypatio
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Undergrad Understanding linear transformation
  • schniefen
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Proving parallel lines using points and vectors
  • algebruh
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Graduate Three dimensional Lie algebra L with dim L' = 1
  • valtz
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Undergrad Master the Eigenvalue Algorithm for Math GRE Exams
  • brydustin
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Graduate Operator in a real vector space has an upper block triangular matrix
  • vish_maths
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Graduate Proof of Maximal Left Ideal Generation in the Ring Mn(F)
  • xixi
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Graduate Implicit Runge–Kutta in R^3 space
  • Beduino
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1
Graduate Operations on Ideals - Hello Experts
  • DukeSteve
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Graduate Reducing Rank-3 Tensor Field into Matrix
  • Kreizhn
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1
Graduate What Are the Kernels of Robotic Solving Methods in Infinite Differentiability?
  • DanielThrice
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Graduate Understanding the Principle of Lifting Invariants in Lie Algebras
  • Office_Shredder
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Graduate Do Left and Right Semisimplicity Coincide in Non-Unital Rings?
  • Ruslan_Sharipov
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Graduate Order of Elements in a Group: A Quick Check of Understanding
  • Artusartos
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1
Graduate Variance captured in coordinate axis.
  • simpleton
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Graduate How Do Eigenvectors of Block Covariance Matrices Interrelate?
  • GoodSpirit
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Graduate How Do You Calculate Probabilities with Non-Coprime Residue Classes?
  • CRGreathouse
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Graduate Applying 3 Concurrent Angular Velocities to Vectors
  • Ryoko
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Graduate Can We Approximate the Matrix Square Root of A+B Under Certain Conditions?
  • jostpuur
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Undergrad Rotate a shape back to its original position with the fewest rotations
  • kolleamm
  • · Replies 21 ·
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Undergrad Finding the dimension of the span ##u_1-u_2, ...., u_n-u_1##?
  • schniefen
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2
Invertiable Matrix - explaining it to children - ideas how to teach
  • roni1
  • · Replies 1 ·
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Zero divisor for polynomial rings
  • cbarker1
  • · Replies 1 ·
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1
High School Size of a Vector: Inner Product & Magnitude
  • snoopies622
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Undergrad If T^2 = T, where T is a linear operator on V, T=I or T=0?
  • JJ__
  • · Replies 11 ·
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Undergrad Find the closest distance between two lines segments?
  • kolleamm
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1
Graduate Proving Division of Local Ring in Ring with Idempotents
  • xixi
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1
Graduate Double Dual Example: V=R^2 to V** Transformation
  • Damidami
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Graduate C* algebras, states, finite graphs
  • marcus
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Graduate Exploiting a the inverse to determine eigen vectors?
  • Jonnyb302
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Graduate Multilinear Maps of V^n into Reals and Effect of Linear Transforma
  • WWGD
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Graduate Can the trace be expressed in terms of the determinant?
  • Jhenrique
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Graduate How Can I Catch Up on Field Theory After Being Sick?
  • HardBoiled88
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Graduate Finding Dual Basis of Linear Functionals for a Given Basis in C^3
  • Abuattallah
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Graduate Multiplicative and additive identities as successors
  • pilpel
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Graduate Designating matrices by (system2 operator system1)
  • Lojzek
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Graduate Help with Pojective Linear Groups
  • Phillips101
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Graduate Group Theory and Energy Eigenstates in Quantum Mechanics
  • praharmitra
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1
Graduate What is the dimension of the graph of F?
  • rtgt
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1
Graduate Trying to Develop a Decryption Scheme for a Given Encryption
  • BWElbert
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1
Graduate Rational Numbers That Are Hard To Prove?
  • Office_Shredder
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Undergrad I'm trying to write a program that plots the riemann zeta function
  • LastTimelord
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Graduate Terminology for (anti)symmetric tensors in characteristic 2
  • Hurkyl
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Graduate Proving the Chinese Remainder Theorem for Reduced Residues Modulo mn
  • frowdow
  • · Replies 1 ·
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1
Graduate Non-adjoint Conjugate of Pure State Vector
  • Pythagorean
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Graduate How Does a Quotient Module Relate to Its Generators in a Local Ring?
  • Artusartos
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Graduate Does there exist a transformation between a loop and a close loop ?
  • peter308
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Graduate Reconstructing operator matrix from subspace samples
  • uekstrom
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1
Graduate Orthogonal Subgroups : on Modules?
  • Bacle
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Graduate What is SU*(N)? Definition and Explanation
  • William Nelso
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Graduate Solving: How H Normalises [H,K]?
  • Silversonic
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Graduate Matrix form of Lie algebra highest weight representation
  • vega12
  • · Replies 1 ·
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Graduate Learn a bit more about triality of SO
  • kexue
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Graduate Solve Weird Matrix Equation to Get Values for P
  • maistral
  • · Replies 5 ·
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Graduate Confusion about the definition of adjoint representation and roots.
  • AlbertEi
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Graduate Solving for a Lie Algebra in General
  • pdxautodidact
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Graduate Deriving transformation matrix from clues
  • GooseMunch
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Graduate Solving AM=MB for 3x3 Matrices: Vectorize M & Find 9 Equations
  • daviddoria
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Graduate How Can Orbits Depend on Each Other in Colored Graph Automorphisms?
  • matt42
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Graduate Diagonal Perturbations of Linear Equations
  • JohnSimpson
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Graduate Can Structure Constants Define a Metric in a 10D Lie Algebra?
  • jfy4
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Graduate Different Type of Extension Problem for Groups
  • Hello Kitty
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Graduate Principal component analysis (PCA) with small number of observations
  • miguelcc
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1
Graduate Validity of Direct Product Structure of Symmetry Group
  • Newtime
  • · Replies 1 ·
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Graduate Tensor Products and Maps Factoring Through
  • WWGD
  • · Replies 6 ·
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6
Graduate Calculating an expression for trace of generators of two Lie algebra
  • vnikoofard
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1
Graduate Degree p Invariants in Linear Tensor Products: Bishop & Goldberg, p. 86-87
  • Rasalhague
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Graduate Subalgebra of one less dimension
  • jostpuur
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Graduate How Do Radical Ideals Relate to Submodules in Algebra?
  • alexfloo
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Graduate Can B Be Determined from Given A and C in Kronecker Product?
  • umut_caglar
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Graduate Is There a Name for a Subcategory Acting Like an Ideal in Category Theory?
  • tmatrix
  • · Replies 1 ·
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Graduate Is \alpha in LK determined by polynomials and elements from subfields L and K?
  • winter85
  • · Replies 1 ·
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Graduate Is There an Algorithm for Solving the Combinatorial Design Problem?
  • Constantinos
  • · Replies 1 ·
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1
Graduate Automorphism of these Cayley graphs
  • tsang
  • · Replies 1 ·
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Graduate Find Cartan Subalgebra for Algebra Given Generators
  • CuriosusNN
  • · Replies 1 ·
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1
Undergrad Matrix prerequisities for Gauss elimination
  • Ronankeating
  • · Replies 1 ·
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Graduate Lie algebras contained in Universal Enveloping Algebra
  • Couchyam
  • · Replies 1 ·
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Graduate Linear combinations of structure constants
  • AlphaNumeric2
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Graduate Accurate estimation of complex eigenvalues
  • soikez
  • · Replies 1 ·
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1
Graduate Are FG-Modules More Advantageous Than Group Representations?
  • OMM!
  • · Replies 1 ·
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Graduate Multiplicative groups of nonzero reals and pos. reals
  • Bachelier
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Graduate Is this a route to the prime number theorem?
  • arivero
  • · Replies 1 ·
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1
Graduate Is the T x S^1 action on C^infinity functions free?
  • Firefly!
  • · Replies 1 ·
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Graduate On Finding Lie Algebra Representations
  • antibrane
  • · Replies 1 ·
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1
Undergrad Sparse Matrix transformation to locate columns containing zeros
  • taknevski
  • · Replies 1 ·
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Undergrad Procedure for orking out the basis of the kernel of a linear transformation.
  • sid9221
  • · Replies 1 ·
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1
Graduate Non-Square Skew (Symmetric/Repeating) Matrix?
  • GreenLRan
  • · Replies 1 ·
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1
Graduate Arithmetical function and distributions
  • zetafunction
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Graduate An identity about Gamma and Riemann function
  • zetafunction
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Undergrad Elementary Row Operations and Preserving Solutions.
  • Bacle
  • · Replies 1 ·
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Undergrad Proving Rational Solutions in Linear Systems with Rational Coefficients
  • e(ho0n3
  • · Replies 1 ·
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Graduate Triangle homography is possible I am a first?
  • mrStrange
  • · Replies 16 ·
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Graduate Optimization of objective function that's the product of unitary matrices
  • bastpg
  • · Replies 3 ·
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3
Graduate Equivalence of Unimodular (Quadratic)forms on Abelian groups
  • WWGD
  • · Replies 1 ·
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Graduate Modules with multiple operators
  • cjellison
  • · Replies 1 ·
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1