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 Dimension of a vector space and its subspaces
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Undergrad How does one find the dual of a matrix?
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Undergrad Definition of the special unitary group
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Graduate Can three elbows generate any point in space?
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Undergrad Passive Transformation and Rotation Matrix
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Undergrad How can the dual tensors derivation be achieved using rotation matrices?
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Undergrad Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction
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Undergrad Unravelling Structure of a Symmetric Matrix
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Undergrad Question about vector spaces and subsets
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High School What unique contributions to math did linear algebra make?
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Undergrad Normal Mode calculation steps
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Undergrad About the definition of vector space of infinite dimension
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Undergrad Definition of Clifford Algebras
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Undergrad Do hyperbolic harmonics exist?
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Undergrad Can I visualize O(3) \ SO(3) in some way?
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Undergrad General Linear Group GL(n) on Vector Spaces and canonical pairing invariance
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Graduate What causes a complex symmetric matrix to change from invertible to non-invertible?
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Undergrad Terminologies used to describe tensor product of vector spaces
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Undergrad Non orthogonal basis and the lines of its coordinate grid
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Graduate How to augment a machine learning matrix?
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Undergrad Finding the orthogonal projection of a vector without an orthogonal basis
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Graduate The Klein 4-group
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Graduate Bivariate Smoothing Splines
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Undergrad Standard basis and other bases...
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Undergrad Vector subspace and basis vectors in the context of data science
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Undergrad What Are Classical Lie Algebras A, B, C, and D?
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Undergrad Change of basis matrix for point group C3V
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High School Understanding Bases of a Vector Space
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Graduate How Does U(1) Double-Cover SO(2) for a Specified Angle?
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Undergrad Do Metric Tensors Always Have Inverses?
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Undergrad Question Regarding Definition of Tensor Algebra
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Undergrad Visualization of complex vectors and dot product
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Undergrad Solve the system of linear equations
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High School Confused about dot product multiplication
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Undergrad Local inverse of non bijective functions
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Undergrad Is there always a matrix corresponding to eigenvectors?
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Graduate Spectrum of an algebra (Alain Connes paper)
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High School Parametric Representation of Lines
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Undergrad Help in understanding Eigenvectors please
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Undergrad About permutation acting on the Identity matrix
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Undergrad Number of Binary Operations on a Set with a Special Property
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Undergrad Is There a Connection Between Conjugation and Change of Basis?
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Graduate What are Modular Lie Algebras and How Do They Apply to Function Spaces?
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High School How to multiply matrix with row vector?
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High School Can Shifting Vectors Affect Their Exponential Distance Sum Equality?
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Undergrad Why Use Gram-Schmidt to Make a Unitary Matrix?
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Undergrad Page 183-184 of Howard George's group book
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Undergrad What can be deduced about the roots of this polynomial?
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Undergrad How can I test for positive semi-definiteness in matrices?
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Undergrad Spectral theorem for Hermitian matrices-- special cases
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Graduate Quintic and Higher Degree Polynomial Equations
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Undergrad On a bound on the norm of a matrix with a simple pole
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Graduate Finding dual optimum of a linear problem
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Undergrad Using an array to solve a system of equations
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Undergrad Transfer rank2 tensor to a new basis
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Undergrad Dimension and solution to matrix-vector product
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Undergrad Why do the lines m and l coincide in the proof of the parallelogram rule?
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Undergrad Dot product, inner product, and projections
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Undergrad Row space, Column space, Null space & Left null space
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Undergrad Changes under a rotation around the z-axis by an angle α
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Undergrad Are linear automorphisms nothing but the identity mapping?
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Undergrad Algebra Homomorphisms as Subsets of the Cartesian Product
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Graduate Similarity transformation changing the determinant to 1
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Undergrad Not all reflections in 2D are 3D rotations?
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Undergrad What Is the Customary Definition of Zero Mapping in Set S Mappings?
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Graduate Classification of reductive groups via root datum
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High School Question on basic linear algebra (new to the subject)
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Undergrad Question on Primitive Roots and GCDs
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Graduate Does this construction verify the universal property?
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Undergrad Understanding Hessian for multidimensional function
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Graduate What is a free product of groups or vector space?
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Undergrad Question on invertibility in finite fields
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Undergrad Fourier Transformation on a Ring
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Undergrad What Is a Torsion Element in Ring Theory?
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Undergrad Order of an element in ##\mathbb{Z}_n##
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Undergrad Simplify tensor product statement
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Graduate Computing the Minimal polynomial - Ring Theory
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Undergrad Understanding the operation in ##(\mathbb{z_6})^{*}##
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Undergrad Analogy question for algebraists
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Undergrad Solve the problem involving Rings
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Undergrad Zero Element in a Ring: The 0 Ring Has Only One Element
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Undergrad Problem with notation of matrix elements
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High School Can the Diagram in the Article Be Interpreted as Commutative?
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High School Elementary column operations and change-of-basis
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Undergrad What is the size of the quotient group L/pZ^m?
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Undergrad Proof of vector property in space
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Undergrad Multiplication in projective space
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Undergrad Question from a proof in Axler 2nd Ed, 'Linear Algebra Done Right'
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Graduate Finding Eigenvectors for Two Matrices using the Generalized Jacobi Method
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Graduate Can a Non-Diagonal Hermitian Matrix be Diagonalized Using Unitary Matrix?
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Insights Introduction to the World of Algebras
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Graduate Coefficients of Chebyshev polynomials
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Undergrad Variant of Baker-Campbell-Hausdorff Formula
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Undergrad Isomorphisms between C4 & Z4 Groups
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Undergrad Proof for subgroup -- How prove it is a subgroup of Z^m?
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Undergrad Parallel vector, I need a bit of explanation
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Undergrad Proof regarding congruence relation
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Undergrad Need Help understanding Griffiths [Vector Analysis]
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Undergrad Question on proof ##\Lambda^{\perp}(AU) = U^{-1} \Lambda^{\perp}(A)##
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Graduate About Universal enveloping algebra
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