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 The meaning of ##(ict, x_1,x_2,x_3)##
- mma
- · Replies 4 ·
Graduate Hidden symmetries in subgroups of Lie groups?
- arivero
- · Replies 1 ·
Undergrad The Orthogonality of the Eigenvectors of a 2x2 Hermitian Matrix
- rghurst
- · Replies 13 ·
Graduate The original definition of Category
- billtodd
- · Replies 45 ·
Graduate Why are the eigenvectors of this hermitian matrix not orthogonal?
- rghurst
- · Replies 2 ·
Undergrad Monumental Proof Settles Geometric Langlands Conjecture
- Astronuc
- · Replies 1 ·
Undergrad Equivalence of 2 definitions of the magnitude of the cross product?
- nomadreid
- · Replies 6 ·
Undergrad Matrix diagonalization algorithm
- Spathi
- · Replies 5 ·
Graduate Can anybody please explain in layman terms the super-vector spaces?
- Anixx
- · Replies 3 ·
Undergrad Dimension of a vector space and its subspaces
- Txema
- · Replies 15 ·
Undergrad How does one find the dual of a matrix?
- grzz
- · Replies 14 ·
Undergrad Definition of the special unitary group
- redtree
- · Replies 46 ·
Graduate Can three elbows generate any point in space?
- petersng
- · Replies 7 ·
Undergrad Passive Transformation and Rotation Matrix
- shinobi20
- · Replies 1 ·
Undergrad How can the dual tensors derivation be achieved using rotation matrices?
- euphoricrhino
- · Replies 5 ·
Undergrad Why does the identity permutation always decompose into an even number of transpositions?
- nomadreid
- · Replies 8 ·
Undergrad Unravelling Structure of a Symmetric Matrix
- thatboi
- · Replies 5 ·
Undergrad Can a subset be a vector space without being a subspace?
- green
- · Replies 8 ·
High School What unique contributions to math did linear algebra make?
- NoahsArk
- · Replies 19 ·
Undergrad Normal Mode calculation steps
- vgarg
- · Replies 2 ·
Undergrad About the definition of vector space of infinite dimension
- cianfa72
- · Replies 18 ·
Undergrad Definition of Clifford Algebras
- jv07cs
- · Replies 7 ·
Undergrad Do hyperbolic harmonics exist?
- gerald V
- · Replies 1 ·
Undergrad Can I visualize O(3) \ SO(3) in some way?
- BerriesAndCream
- · Replies 4 ·
Undergrad General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
- jv07cs
- · Replies 1 ·
Graduate What causes a complex symmetric matrix to change from invertible to non-invertible?
- Tybalt
- · Replies 5 ·
Undergrad Terminologies used to describe tensor product of vector spaces
- cianfa72
- · Replies 7 ·
Undergrad Non orthogonal basis and the lines of its coordinate grid
- fog37
- · Replies 9 ·
Graduate How to augment a machine learning matrix?
- strat468
- · Replies 10 ·
Undergrad Finding the orthogonal projection of a vector without an orthogonal basis
- AimaneSN
- · Replies 3 ·
Graduate The Klein 4-group
- Anko
- · Replies 10 ·
Graduate Bivariate Smoothing Splines
- Joe Prendergast
- · Replies 1 ·
Undergrad Why orthogonal bases don't need other basis vectors to find coefficients
- fog37
- · Replies 9 ·
Undergrad Vector subspace and basis vectors in the context of data science
- DumpmeAdrenaline
- · Replies 6 ·
Undergrad What Are Classical Lie Algebras A, B, C, and D?
- HDB1
- · Replies 4 ·
Undergrad Change of basis matrix for point group C3V
- knowwhatyoudontknow
- · Replies 2 ·
High School Understanding Bases of a Vector Space
- NoahsArk
- · Replies 3 ·
Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
- pellis
- · Replies 2 ·
Undergrad Do Metric Tensors Always Have Inverses?
- jv07cs
- · Replies 8 ·
Undergrad Question Regarding Definition of Tensor Algebra
- jv07cs
- · Replies 10 ·
Undergrad Visualization of complex vectors and dot product
- Mike_bb
- · Replies 14 ·
Undergrad Solve the system of linear equations
- chwala
- · Replies 2 ·
High School What does the dot product result represent geometrically?
- NoahsArk
- · Replies 33 ·
Undergrad Local inverse of non bijective functions
- S123456
- · Replies 9 ·
Undergrad Is there always a matrix corresponding to eigenvectors?
- NotEuler
- · Replies 24 ·
Graduate Spectrum of an algebra (Alain Connes paper)
- Heidi
- · Replies 19 ·
High School Parametric Representation of Lines
- NoahsArk
- · Replies 13 ·
Undergrad Finding eigenvectors from the characteristic equation
- Martyn Arthur
- · Replies 22 ·
Undergrad About permutation acting on the Identity matrix
- aalma
- · Replies 7 ·
Undergrad Number of Binary Operations on a Set with a Special Property
- Expiring
- · Replies 2 ·
Undergrad Connection between matrix conjugation and the adjoint representation in Lie groups
- knowwhatyoudontknow
- · Replies 1 ·
Graduate What are Modular Lie Algebras and How Do They Apply to Function Spaces?
- dx
- · Replies 5 ·
High School How to multiply matrix with row vector?
- entropy1
- · Replies 4 ·
High School Can Shifting Vectors Affect Their Exponential Distance Sum Equality?
- thatboi
- · Replies 3 ·
Undergrad Why Use Gram-Schmidt to Make a Unitary Matrix?
- nomadreid
- · Replies 14 ·
Undergrad Page 183-184 of Howard George's group book
- LCSphysicist
- · Replies 1 ·
Undergrad What can be deduced about the roots of this polynomial?
- Dowland
- · Replies 3 ·
Undergrad How can I test for positive semi-definiteness in matrices?
- Trollfaz
- · Replies 1 ·
Undergrad Spectral theorem for Hermitian matrices-- special cases
- nomadreid
- · Replies 2 ·
Graduate Quintic and Higher Degree Polynomial Equations
- Pikkugnome
- · Replies 3 ·
Undergrad On a bound on the norm of a matrix with a simple pole
- psie
- · Replies 8 ·
Undergrad Using an array to solve a system of equations
- barryj
- · Replies 7 ·
Undergrad Transfer rank2 tensor to a new basis
- GGGGc
- · Replies 2 ·
Undergrad Dimension and solution to matrix-vector product
- DumpmeAdrenaline
- · Replies 4 ·
Undergrad Why do the lines m and l coincide in the proof of the parallelogram rule?
- PLAGUE
- · Replies 4 ·
Undergrad Dot product, inner product, and projections
- nomadreid
- · Replies 7 ·
Undergrad Do linearly independent rows form a basis for the row space?
- DumpmeAdrenaline
- · Replies 8 ·
Undergrad Changes under a rotation around the z-axis by an angle α
- NODARman
- · Replies 1 ·
Undergrad Are linear automorphisms nothing but the identity mapping?
- William Crawford
- · Replies 6 ·
Undergrad Algebra Homomorphisms as Subsets of the Cartesian Product
- Migushiby
- · Replies 2 ·
Graduate Similarity transformation changing the determinant to 1
- spin_100
- · Replies 20 ·
Undergrad Why can't 2D reflection across y=x be represented as a 3D rotation?
- nomadreid
- · Replies 9 ·
Undergrad What Is the Customary Definition of Zero Mapping in Set S Mappings?
- Stephen Tashi
- · Replies 8 ·
Graduate Classification of reductive groups via root datum
- The Tortoise-Man
- · Replies 3 ·
High School Question on basic linear algebra (new to the subject)
- TheJohn
- · Replies 10 ·
Undergrad Question on Primitive Roots and GCDs
- Albert01
- · Replies 2 ·
Graduate Does this construction verify the universal property?
- Heidi
- · Replies 7 ·
Undergrad Understanding Hessian for multidimensional function
- SaschaSIGI
- · Replies 1 ·
Graduate What is a free product of groups or vector space?
- Heidi
- · Replies 2 ·
Undergrad Question on invertibility in finite fields
- Albert01
- · Replies 4 ·
Undergrad Fourier Transformation on a Ring
- Albert01
- · Replies 11 ·
Undergrad What Is a Torsion Element in Ring Theory?
- Stephen Tashi
- · Replies 13 ·
Undergrad Order of an element in ##\mathbb{Z}_n##
- chwala
- · Replies 7 ·
Undergrad Simplify tensor product statement
- Albert01
- · Replies 1 ·
Graduate Computing the Minimal polynomial - Ring Theory
- chwala
- · Replies 4 ·
Undergrad Units in Z/6Z and Z/5Z under multiplication
- chwala
- · Replies 6 ·
Undergrad Analogy question for algebraists
- Stephen Tashi
- · Replies 1 ·
Undergrad Solve the problem involving Rings
- chwala
- · Replies 5 ·
Undergrad Zero Element in a Ring: The 0 Ring Has Only One Element
- chwala
- · Replies 1 ·
Undergrad Problem with notation of matrix elements
- Lambda96
- · Replies 3 ·
High School Can the Diagram in the Article Be Interpreted as Commutative?
- Stephen Tashi
- · Replies 3 ·
High School Elementary column operations and change-of-basis
- Stephen Tashi
- · Replies 7 ·
Undergrad What is the size of the quotient group L/pZ^m?
- Albert01
- · Replies 1 ·
Undergrad Proof of vector property in space
- chwala
- · Replies 9 ·
Undergrad Multiplication in projective space
- Structure seeker
- · Replies 7 ·
Undergrad Question from a proof in Axler 2nd Ed, 'Linear Algebra Done Right'
- Stephen Tashi
- · Replies 3 ·
Graduate Finding Eigenvectors for Two Matrices using the Generalized Jacobi Method
- hoshangmustafa
- · Replies 7 ·
Graduate Can a Non-Diagonal Hermitian Matrix be Diagonalized Using Unitary Matrix?
- LagrangeEuler
- · Replies 9 ·
Insights Introduction to the World of Algebras
- fresh_42
- · Replies 0 ·
Graduate Coefficients of Chebyshev polynomials
- gty656
- · Replies 2 ·