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 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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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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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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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 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 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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Undergrad A wonderful flow chart for taxonomy of matrices
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Undergrad Find the Eigenvalues and eigenvectors of 3x3 matrix
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Graduate Questions about solvable Lie algebras
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Graduate Understanding the Second Direction in Semi Simple Lie Algebra
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Undergrad Is the Order of an Automorphism in a Field with Characteristic p Equal to p?
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Graduate What is the definition of quotient Lie algebra?
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Graduate About Schur's lemma in lie algebra
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Graduate About universal enveloping algebra
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About semidirect product of Lie algebra
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How to compute the Casimir element of Lie algebra sl(2)?
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Graduate Proving Cartan Subalgebra $\mathbb{K} H$ is Self-Normalizer
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Graduate How Do We Prove ##L / Z(L)## is Nilpotent in Engel's Theorem?
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Graduate How do we prove that a nonzero nilpotent Lie algebra has a nontrivial center?
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Undergrad About derivations of lie algebra
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