Linear and Abstract Algebra Forum

Post thread
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.
Graduate About Universal enveloping algebra
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad A wonderful flow chart for taxonomy of matrices
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Find the Eigenvalues and eigenvectors of 3x3 matrix
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Questions about solvable Lie algebras
  • · Replies 7 ·
Replies
7
Views
3K
High School Attempt to solve this system of three linear equations
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Understanding the Second Direction in Semi Simple Lie Algebra
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Is the Order of an Automorphism in a Field with Characteristic p Equal to p?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate What is the definition of quotient Lie algebra?
  • · Replies 15 ·
Replies
15
Views
3K
Graduate About Schur's lemma in lie algebra
  • · Replies 2 ·
Replies
2
Views
3K
Graduate About universal enveloping algebra
  • · Replies 19 ·
Replies
19
Views
3K
Graduate About semidirect product of Lie algebra
  • · Replies 19 ·
Replies
19
Views
3K
Graduate How to compute the Casimir element of Lie algebra sl(2)?
  • · Replies 24 ·
Replies
24
Views
4K
Graduate Proving Cartan Subalgebra $\mathbb{K} H$ is Self-Normalizer
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How Do We Prove ##L / Z(L)## is Nilpotent in Engel's Theorem?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How do we prove that a nonzero nilpotent Lie algebra has a nontrivial center?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad About derivations of lie algebra
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Proving SL_2(C) Homeomorphic to SU(2)xT & Simple Connectedness
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Proof of Column Extraction Theorem for Finding a Basis for Col(A)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Smallest subspace if a plane and a line are passing through the origin
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Using the orbit-stabilizer theorem to identify groups
  • · Replies 11 ·
Replies
11
Views
3K
High School Solving for the Nth divergence in any coordinate system
  • · Replies 41 ·
2
Replies
41
Views
5K
High School Row reduction, Gaussian Elimination on augmented matrix
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Anti-unitary operators and the Hermitian conjugate
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Tensor decomposition, Sym representations and irreps.
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Need help understanding Commuting Operators
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Finite many Lattice Points in Sphere?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Bra-Ket Notation Manipulations: Quantum State Expansion
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad About writing a unitary matrix in another way
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Derivation of Cauchy-Schwarz Inequality
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Geometric Algebra: Rejection of one blade in another
  • · Replies 11 ·
Replies
11
Views
4K
Undergrad Absolute value bars in dot product derivation
  • · Replies 2 ·
Replies
2
Views
3K
High School Vector Calculus in 1D: ± to Show Magnitude?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Law of Cosines in Linear Algebra: Understanding the Dot Product of Unit Vectors
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Question regarding fundamental region of a lattice
  • · Replies 20 ·
Replies
20
Views
3K
Graduate How to take a matrix outside the diagonal operator?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad What are double cosets in group theory?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad If T is diagonalizable then is restriction operator diagonalizable?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Solve a nonlinear matrix equation
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Cycles from patterns in a permutation matrix
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Adjacent transpositions: question about definition
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Show ##sup\{a \in \mathbb{Q}: a^2 \leq 3\} = \sqrt{3}##
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Completeness of the formal power series and valued fields
  • · Replies 2 ·
Replies
2
Views
2K
High School Transformation Rules For A General Tensor M
  • · Replies 1 ·
Replies
1
Views
2K
High School Question about orthogonal vectors and the cosine
  • · Replies 5 ·
Replies
5
Views
2K
High School Array Representation Of A General Tensor Question
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Orthonormal basis expression for ordinary contraction of a tensor
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad A = norm-preserving linear map (+other conditions) => A = lin isometry
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Consistent matrix index notation when dealing with change of basis
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Question about implication from scalar product
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Properties of Lattice Projections
  • · Replies 23 ·
Replies
23
Views
3K
High School Beginner Einstein Notation Question On Summation In Regards To Index
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Smoothing algorithm for real-world data
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad Frequency of prime number gaps according to (p-1)/(p-2)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How to do algebra on the Kitaev toric code grid?
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Why is the dual of Z^n again Z^n ?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate How Does Induced Mapping Function in Algebraic Topology?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Determining elements of Markov matrix from a known stationary vector
  • · Replies 24 ·
Replies
24
Views
3K
Graduate What is the generator of the cyclic group (Z,+)?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Parallel and perpendicular components
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad The Price of Beer - Linear Algebra Problem
  • · Replies 44 ·
2
Replies
44
Views
5K
Undergrad Full Course in Group Theory (and More) on YouTube
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Unitary Operator: Can X Make L(A) Unitary?
  • · Replies 17 ·
Replies
17
Views
2K
Graduate Are the numbers ##eπ## and ##e+ π## transcendental?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Is this a typo or am I missing something? (polynomial equations)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Getting eigenvalues of an arbitrary matrix with programming
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What group might represent the symmetries of these carbon rings?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Proof of the inequality of a reduced basis
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Does a set of matrices form a ring? Or what is the algebraic structure?
  • · Replies 24 ·
Replies
24
Views
4K
High School Elegant way to prove ##AB^{n}## commute
  • · Replies 1 ·
Replies
1
Views
1K
High School Turn one vector into another vector
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Group like operations that are not associative
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Transform a 2x2 matrix into an anti-symmetric matrix
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is the solution to this problem as trivial as I think?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Algebra equation with variable as exponent
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Existence and Uniqueness of Inverses
  • · Replies 5 ·
Replies
5
Views
2K
Insights Évariste Galois and His Theory
  • · Replies 28 ·
Replies
28
Views
4K
Undergrad How Does the Successive Minima of a Lattice Compare to Basis Vectors?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad How can I convince myself that I can find the inverse of this matrix?
  • · Replies 34 ·
2
Replies
34
Views
3K
Undergrad Is -1 in U=eiA an Exponent or an Inverse?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Question about algebraic transformation
  • · Replies 25 ·
Replies
25
Views
3K
Graduate Question regarding proof of convex body theorem
  • · Replies 21 ·
Replies
21
Views
2K
MHB Transformation of a Line Segment
  • · Replies 6 ·
Replies
6
Views
3K
MHB Question from Kamal about Gaussian Elimination via email
  • · Replies 1 ·
Replies
1
Views
5K
MHB Difference Between Tensor Product and Outer Product
  • · Replies 1 ·
Replies
1
Views
4K
MHB Find the equation of the plane given a point and two planes
  • · Replies 1 ·
Replies
1
Views
3K
MHB Sava's question via email about symmetric matrices
  • · Replies 1 ·
Replies
1
Views
6K
MHB Sava's question via email about matrix multiplication
  • · Replies 1 ·
Replies
1
Views
6K
MHB Jamal's Q via email solving a system
  • · Replies 1 ·
Replies
1
Views
5K
MHB Saqifriends's Question from Math Help Forum
  • · Replies 1 ·
Replies
1
Views
4K
MHB Effie's question via email about Eigenvalues, Eigenvectors and Diagonalisation
  • · Replies 1 ·
Replies
1
Views
5K
MHB Tensor Products - Dummit and Foote - Section 10-4, pages 359 - 362
  • · Replies 1 ·
Replies
1
Views
3K
MHB Is Gauss' Lemma the Key to Non-UFDs in Polynomial Rings?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Mason's question via Facebook about solving a system of equations
  • · Replies 1 ·
Replies
1
Views
11K
Undergrad What Is the Study of Homomorphisms from Abstract Groups to GL(n)?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad The limit of the perimeter of a Koch snowflake as s(0) goes to zero
  • · Replies 10 ·
Replies
10
Views
2K
MHB Finding z-(1/z) Given z=r(cosx+isinx)
  • · Replies 6 ·
Replies
6
Views
2K
MHB Is z + z¯ and z × z¯ Real for Any Complex Number z?
  • · Replies 1 ·
Replies
1
Views
1K
MHB How Do You Solve These Simultaneous Equations?
  • · Replies 2 ·
Replies
2
Views
1K