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.
Undergrad Proof for subgroup -- How prove it is a subgroup of Z^m?
  • Peter_Newman
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Undergrad Parallel vector, I need a bit of explanation
  • lioric
  • · Replies 4 ·
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4
Undergrad Proof regarding congruence relation
  • Peter_Newman
  • · Replies 4 ·
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4
Undergrad Need Help understanding Griffiths [Vector Analysis]
  • Slimy0233
  • · Replies 20 ·
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20
Undergrad Question on proof ##\Lambda^{\perp}(AU) = U^{-1} \Lambda^{\perp}(A)##
  • Peter_Newman
  • · Replies 2 ·
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2
Graduate About Universal enveloping algebra
  • HDB1
  • · Replies 4 ·
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4
Undergrad A wonderful flow chart for taxonomy of matrices
  • swampwiz
  • · Replies 1 ·
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1
Undergrad Find the Eigenvalues and eigenvectors of 3x3 matrix
  • Michael_0039
  • · Replies 12 ·
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12
Graduate Questions about solvable Lie algebras
  • HDB1
  • · Replies 7 ·
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7
High School Attempt to solve this system of three linear equations
  • Elara04
  • · Replies 10 ·
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10
Graduate Understanding the Second Direction in Semi Simple Lie Algebra
  • HDB1
  • · Replies 9 ·
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9
Undergrad Is the Order of an Automorphism in a Field with Characteristic p Equal to p?
  • HDB1
  • · Replies 2 ·
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2
Graduate What is the definition of quotient Lie algebra?
  • HDB1
  • · Replies 15 ·
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Graduate About Schur's lemma in lie algebra
  • HDB1
  • · Replies 2 ·
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2
Graduate About universal enveloping algebra
  • HDB1
  • · Replies 19 ·
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19
Graduate About semidirect product of Lie algebra
  • HDB1
  • · Replies 19 ·
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19
Graduate How to compute the Casimir element of Lie algebra sl(2)?
  • HDB1
  • · Replies 24 ·
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24
Graduate Proving Cartan Subalgebra $\mathbb{K} H$ is Self-Normalizer
  • HDB1
  • · Replies 4 ·
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4
Graduate How Do We Prove ##L / Z(L)## is Nilpotent in Engel's Theorem?
  • HDB1
  • · Replies 4 ·
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4
Graduate How do we prove that a nonzero nilpotent Lie algebra has a nontrivial center?
  • HDB1
  • · Replies 9 ·
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9
Undergrad About derivations of lie algebra
  • HDB1
  • · Replies 5 ·
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5
Undergrad Proving SL_2(C) Homeomorphic to SU(2)xT & Simple Connectedness
  • aalma
  • · Replies 1 ·
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1
Undergrad Proof of Column Extraction Theorem for Finding a Basis for Col(A)
  • mattTch
  • · Replies 3 ·
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3
Undergrad Want to understand how to express the derivative as a matrix
  • nomadreid
  • · Replies 8 ·
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8
Undergrad Smallest subspace if a plane and a line are passing through the origin
  • sindhuja
  • · Replies 2 ·
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2
Undergrad Using the orbit-stabilizer theorem to identify groups
  • aalma
  • · Replies 11 ·
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11
High School Solving for the Nth divergence in any coordinate system
  • Vanilla Gorilla
  • · Replies 41 ·
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High School Row reduction, Gaussian Elimination on augmented matrix
  • Rafa3D
  • · Replies 6 ·
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6
Undergrad Anti-unitary operators and the Hermitian conjugate
  • pellman
  • · Replies 2 ·
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2
Undergrad Tensor decomposition, Sym representations and irreps.
  • knowwhatyoudontknow
  • · Replies 1 ·
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1
Undergrad Need help understanding Commuting Operators
  • expos4ever
  • · Replies 6 ·
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6
Undergrad Finite many Lattice Points in Sphere?
  • Peter_Newman
  • · Replies 7 ·
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7
Undergrad Bra-Ket Notation Manipulations: Quantum State Expansion
  • expos4ever
  • · Replies 8 ·
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8
Undergrad About writing a unitary matrix in another way
  • aalma
  • · Replies 3 ·
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3
Undergrad Derivation of Cauchy-Schwarz Inequality
  • member 731016
  • · Replies 14 ·
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14
Undergrad Geometric Algebra: Rejection of one blade in another
  • Hiero
  • · Replies 11 ·
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11
Undergrad Absolute value bars in dot product derivation
  • member 731016
  • · Replies 2 ·
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2
High School Vector Calculus in 1D: ± to Show Magnitude?
  • MatinSAR
  • · Replies 7 ·
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7
Undergrad Law of Cosines in Linear Algebra: Understanding the Dot Product of Unit Vectors
  • TGV320
  • · Replies 10 ·
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10
Undergrad Question regarding fundamental region of a lattice
  • Peter_Newman
  • · Replies 20 ·
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20
Graduate How to take a matrix outside the diagonal operator?
  • Umesh
  • · Replies 5 ·
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5
Undergrad What are double cosets in group theory?
  • Heidi
  • · Replies 4 ·
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4
Undergrad If T is diagonalizable then is restriction operator diagonalizable?
  • CGandC
  • · Replies 3 ·
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3
Graduate Solve a nonlinear matrix equation
  • rehan_eme
  • · Replies 12 ·
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12
Undergrad Cycles from patterns in a permutation matrix
  • nomadreid
  • · Replies 3 ·
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3
Undergrad Adjacent transpositions: question about definition
  • nomadreid
  • · Replies 4 ·
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4
Undergrad Show ##sup\{a \in \mathbb{Q}: a^2 \leq 3\} = \sqrt{3}##
  • JVEK7713
  • · Replies 4 ·
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4
Graduate Completeness of the formal power series and valued fields
  • aalma
  • · Replies 2 ·
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2
High School Transformation Rules For A General Tensor M
  • Vanilla Gorilla
  • · Replies 1 ·
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1
High School Question about orthogonal vectors and the cosine
  • Peter_Newman
  • · Replies 5 ·
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5
High School Array Representation Of A General Tensor Question
  • Vanilla Gorilla
  • · Replies 2 ·
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2
Undergrad Orthonormal basis expression for ordinary contraction of a tensor
  • Shirish
  • · Replies 2 ·
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2
Undergrad A = norm-preserving linear map (+other conditions) => A = lin isometry
  • Shirish
  • · Replies 4 ·
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4
Undergrad Consistent matrix index notation when dealing with change of basis
  • Shirish
  • · Replies 12 ·
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12
Undergrad Question about implication from scalar product
  • Peter_Newman
  • · Replies 19 ·
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19
Undergrad Properties of Lattice Projections
  • Peter_Newman
  • · Replies 23 ·
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23
High School Beginner Einstein Notation Question On Summation In Regards To Index
  • Vanilla Gorilla
  • · Replies 2 ·
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2
Undergrad Smoothing algorithm for real-world data
  • darren0123
  • · Replies 12 ·
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12
Undergrad Frequency of prime number gaps according to (p-1)/(p-2)
  • timmdeeg
  • · Replies 2 ·
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2
Undergrad How to do algebra on the Kitaev toric code grid?
  • James1238765
  • · Replies 18 ·
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18
Undergrad Why is the dual of Z^n again Z^n ?
  • Peter_Newman
  • · Replies 13 ·
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13
Graduate How Does Induced Mapping Function in Algebraic Topology?
  • srgmath2905
  • · Replies 2 ·
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2
Undergrad Determining elements of Markov matrix from a known stationary vector
  • Adel Makram
  • · Replies 24 ·
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24
Graduate What is the generator of the cyclic group (Z,+)?
  • LagrangeEuler
  • · Replies 7 ·
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7
Undergrad Parallel and perpendicular components
  • Portuga
  • · Replies 7 ·
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7
Undergrad The Price of Beer - Linear Algebra Problem
  • diegogarcia
  • · Replies 44 ·
2
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Undergrad Full Course in Group Theory (and More) on YouTube
  • caffeinemachine
  • · Replies 7 ·
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7
Undergrad Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
  • CGandC
  • · Replies 7 ·
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7
Undergrad Unitary Operator: Can X Make L(A) Unitary?
  • nojojo121
  • · Replies 17 ·
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17
Graduate Are the numbers ##eπ## and ##e+ π## transcendental?
  • chwala
  • · Replies 6 ·
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6
Undergrad Is this a typo or am I missing something? (polynomial equations)
  • bigmike94
  • · Replies 6 ·
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6
Undergrad Getting eigenvalues of an arbitrary matrix with programming
  • Trollfaz
  • · Replies 1 ·
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1
Undergrad What group might represent the symmetries of these carbon rings?
  • askmathquestions
  • · Replies 1 ·
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1
Graduate Proof of the inequality of a reduced basis
  • Peter_Newman
  • · Replies 7 ·
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7
Undergrad Does a set of matrices form a ring? Or what is the algebraic structure?
  • askmathquestions
  • · Replies 24 ·
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24
High School Elegant way to prove ##AB^{n}## commute
  • askmathquestions
  • · Replies 1 ·
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1
High School Turn one vector into another vector
  • askmathquestions
  • · Replies 4 ·
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4
Undergrad Group like operations that are not associative
  • pervect
  • · Replies 3 ·
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3
Undergrad Transform a 2x2 matrix into an anti-symmetric matrix
  • dRic2
  • · Replies 5 ·
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5
Undergrad Is the solution to this problem as trivial as I think?
  • PhysicsRock
  • · Replies 4 ·
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4
Undergrad Algebra equation with variable as exponent
  • adamaero
  • · Replies 7 ·
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7
Undergrad Existence and Uniqueness of Inverses
  • jolly_math
  • · Replies 5 ·
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5
Insights Évariste Galois and His Theory
  • fresh_42
  • · Replies 28 ·
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28
Undergrad How Does the Successive Minima of a Lattice Compare to Basis Vectors?
  • Peter_Newman
  • · Replies 8 ·
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8
Undergrad How can I convince myself that I can find the inverse of this matrix?
  • Hall
  • · Replies 34 ·
2
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34
Undergrad Is -1 in U=eiA an Exponent or an Inverse?
  • dyn
  • · Replies 7 ·
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7
Undergrad Question about algebraic transformation
  • Peter_Newman
  • · Replies 25 ·
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25
Graduate Question regarding proof of convex body theorem
  • Peter_Newman
  • · Replies 21 ·
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21
Transformation of a Line Segment
  • bwpbruce
  • · Replies 6 ·
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6
Question from Kamal about Gaussian Elimination via email
  • Prove It
  • · Replies 1 ·
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1
Difference Between Tensor Product and Outer Product
  • Sudharaka
  • · Replies 1 ·
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1
Find the equation of the plane given a point and two planes
  • sawdee
  • · Replies 1 ·
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1
Sava's question via email about symmetric matrices
  • Prove It
  • · Replies 1 ·
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1
Sava's question via email about matrix multiplication
  • Prove It
  • · Replies 1 ·
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1
Jamal's Q via email solving a system
  • Prove It
  • · Replies 1 ·
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1
Saqifriends's Question from Math Help Forum
  • Sudharaka
  • · Replies 1 ·
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1
Effie's question via email about Eigenvalues, Eigenvectors and Diagonalisation
  • Prove It
  • · Replies 1 ·
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1
Tensor Products - Dummit and Foote - Section 10-4, pages 359 - 362
  • Math Amateur
  • · Replies 1 ·
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1
Is Gauss' Lemma the Key to Non-UFDs in Polynomial Rings?
  • Math Amateur
  • · Replies 1 ·
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1
Mason's question via Facebook about solving a system of equations
  • Prove It
  • · Replies 1 ·
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1