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 The Orthogonality of the Eigenvectors of a 2x2 Hermitian Matrix
  • rghurst
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Graduate The original definition of Category
  • billtodd
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Graduate Why are the eigenvectors of this hermitian matrix not orthogonal?
  • rghurst
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Undergrad Monumental Proof Settles Geometric Langlands Conjecture
  • Astronuc
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Undergrad Equivalence of 2 definitions of the magnitude of the cross product?
  • nomadreid
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Undergrad Matrix diagonalization algorithm
  • Spathi
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Graduate Can anybody please explain in layman terms the super-vector spaces?
  • Anixx
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Undergrad Dimension of a vector space and its subspaces
  • Txema
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Undergrad How does one find the dual of a matrix?
  • grzz
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Undergrad Definition of the special unitary group
  • redtree
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Graduate Can three elbows generate any point in space?
  • petersng
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Undergrad Passive Transformation and Rotation Matrix
  • shinobi20
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Undergrad How can the dual tensors derivation be achieved using rotation matrices?
  • euphoricrhino
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Undergrad Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction
  • nomadreid
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Undergrad Unravelling Structure of a Symmetric Matrix
  • thatboi
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Undergrad Question about vector spaces and subsets
  • green
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High School What unique contributions to math did linear algebra make?
  • NoahsArk
  • · Replies 19 ·
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Undergrad Normal Mode calculation steps
  • vgarg
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Undergrad About the definition of vector space of infinite dimension
  • cianfa72
  • · Replies 18 ·
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Undergrad Definition of Clifford Algebras
  • jv07cs
  • · Replies 7 ·
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7
Undergrad Do hyperbolic harmonics exist?
  • gerald V
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Undergrad Can I visualize O(3) \ SO(3) in some way?
  • BerriesAndCream
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Undergrad General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
  • jv07cs
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Graduate What causes a complex symmetric matrix to change from invertible to non-invertible?
  • Tybalt
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Undergrad Terminologies used to describe tensor product of vector spaces
  • cianfa72
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Undergrad Non orthogonal basis and the lines of its coordinate grid
  • fog37
  • · Replies 9 ·
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Graduate How to augment a machine learning matrix?
  • strat468
  • · Replies 10 ·
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10
Undergrad Finding the orthogonal projection of a vector without an orthogonal basis
  • AimaneSN
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Graduate The Klein 4-group
  • Anko
  • · Replies 10 ·
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Graduate Bivariate Smoothing Splines
  • Joe Prendergast
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Undergrad Standard basis and other bases...
  • fog37
  • · Replies 9 ·
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9
Undergrad Vector subspace and basis vectors in the context of data science
  • DumpmeAdrenaline
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6
Undergrad What Are Classical Lie Algebras A, B, C, and D?
  • HDB1
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4
Undergrad Change of basis matrix for point group C3V
  • knowwhatyoudontknow
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High School Understanding Bases of a Vector Space
  • NoahsArk
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Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
  • pellis
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Undergrad Do Metric Tensors Always Have Inverses?
  • jv07cs
  • · Replies 8 ·
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Undergrad Question Regarding Definition of Tensor Algebra
  • jv07cs
  • · Replies 10 ·
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Undergrad Visualization of complex vectors and dot product
  • Mike_bb
  • · Replies 14 ·
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Undergrad Solve the system of linear equations
  • chwala
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High School Confused about dot product multiplication
  • NoahsArk
  • · Replies 33 ·
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Undergrad Local inverse of non bijective functions
  • S123456
  • · Replies 9 ·
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9
Undergrad Is there always a matrix corresponding to eigenvectors?
  • NotEuler
  • · Replies 24 ·
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24
Graduate Spectrum of an algebra (Alain Connes paper)
  • Heidi
  • · Replies 19 ·
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High School Parametric Representation of Lines
  • NoahsArk
  • · Replies 13 ·
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Undergrad Help in understanding Eigenvectors please
  • Martyn Arthur
  • · Replies 22 ·
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Undergrad About permutation acting on the Identity matrix
  • aalma
  • · Replies 7 ·
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7
Undergrad Number of Binary Operations on a Set with a Special Property
  • Expiring
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2
Undergrad Is There a Connection Between Conjugation and Change of Basis?
  • knowwhatyoudontknow
  • · Replies 1 ·
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Graduate What are Modular Lie Algebras and How Do They Apply to Function Spaces?
  • dx
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High School How to multiply matrix with row vector?
  • entropy1
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High School Can Shifting Vectors Affect Their Exponential Distance Sum Equality?
  • thatboi
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Undergrad Why Use Gram-Schmidt to Make a Unitary Matrix?
  • nomadreid
  • · Replies 14 ·
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Undergrad Page 183-184 of Howard George's group book
  • LCSphysicist
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Undergrad What can be deduced about the roots of this polynomial?
  • Dowland
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3
Undergrad How can I test for positive semi-definiteness in matrices?
  • Trollfaz
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Undergrad Spectral theorem for Hermitian matrices-- special cases
  • nomadreid
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Graduate Quintic and Higher Degree Polynomial Equations
  • Pikkugnome
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Undergrad On a bound on the norm of a matrix with a simple pole
  • psie
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8
Undergrad Using an array to solve a system of equations
  • barryj
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7
Undergrad Transfer rank2 tensor to a new basis
  • GGGGc
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Undergrad Dimension and solution to matrix-vector product
  • DumpmeAdrenaline
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4
Undergrad Why do the lines m and l coincide in the proof of the parallelogram rule?
  • PLAGUE
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Undergrad Dot product, inner product, and projections
  • nomadreid
  • · Replies 7 ·
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Undergrad Row space, Column space, Null space & Left null space
  • DumpmeAdrenaline
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Undergrad Changes under a rotation around the z-axis by an angle α
  • NODARman
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Undergrad Are linear automorphisms nothing but the identity mapping?
  • William Crawford
  • · Replies 6 ·
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Undergrad Algebra Homomorphisms as Subsets of the Cartesian Product
  • Migushiby
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Graduate Similarity transformation changing the determinant to 1
  • spin_100
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Undergrad Not all reflections in 2D are 3D rotations?
  • nomadreid
  • · Replies 9 ·
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Undergrad What Is the Customary Definition of Zero Mapping in Set S Mappings?
  • Stephen Tashi
  • · Replies 8 ·
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Graduate Classification of reductive groups via root datum
  • The Tortoise-Man
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High School Question on basic linear algebra (new to the subject)
  • TheJohn
  • · Replies 10 ·
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Undergrad Question on Primitive Roots and GCDs
  • Albert01
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Graduate Does this construction verify the universal property?
  • Heidi
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Undergrad Understanding Hessian for multidimensional function
  • SaschaSIGI
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Graduate What is a free product of groups or vector space?
  • Heidi
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Undergrad Question on invertibility in finite fields
  • Albert01
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Undergrad Fourier Transformation on a Ring
  • Albert01
  • · Replies 11 ·
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Undergrad What Is a Torsion Element in Ring Theory?
  • Stephen Tashi
  • · Replies 13 ·
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Undergrad Order of an element in ##\mathbb{Z}_n##
  • chwala
  • · Replies 7 ·
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Undergrad Simplify tensor product statement
  • Albert01
  • · Replies 1 ·
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Graduate Computing the Minimal polynomial - Ring Theory
  • chwala
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Undergrad Understanding the operation in ##(\mathbb{z_6})^{*}##
  • chwala
  • · Replies 6 ·
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Undergrad Analogy question for algebraists
  • Stephen Tashi
  • · Replies 1 ·
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Undergrad Solve the problem involving Rings
  • chwala
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5
Undergrad Zero Element in a Ring: The 0 Ring Has Only One Element
  • chwala
  • · Replies 1 ·
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Undergrad Problem with notation of matrix elements
  • Lambda96
  • · Replies 3 ·
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High School Can the Diagram in the Article Be Interpreted as Commutative?
  • Stephen Tashi
  • · Replies 3 ·
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High School Elementary column operations and change-of-basis
  • Stephen Tashi
  • · Replies 7 ·
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Undergrad What is the size of the quotient group L/pZ^m?
  • Albert01
  • · Replies 1 ·
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Undergrad Proof of vector property in space
  • chwala
  • · Replies 9 ·
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Undergrad Multiplication in projective space
  • Structure seeker
  • · Replies 7 ·
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7
Undergrad Question from a proof in Axler 2nd Ed, 'Linear Algebra Done Right'
  • Stephen Tashi
  • · Replies 3 ·
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Graduate Finding Eigenvectors for Two Matrices using the Generalized Jacobi Method
  • hoshangmustafa
  • · Replies 7 ·
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Graduate Can a Non-Diagonal Hermitian Matrix be Diagonalized Using Unitary Matrix?
  • LagrangeEuler
  • · Replies 9 ·
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Insights Introduction to the World of Algebras
  • fresh_42
  • · Replies 0 ·
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Graduate Coefficients of Chebyshev polynomials
  • gty656
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Undergrad Variant of Baker-Campbell-Hausdorff Formula
  • thatboi
  • · Replies 3 ·
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3
Undergrad Isomorphisms between C4 & Z4 Groups
  • JackNicholson
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