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.
MHB A Basic Question Regarding the Universal Property of the Tensor Product.
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Graduate Alternate expression for definition of an Ideal?
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Undergrad Structure of a Matrix With Empty Null Space
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Graduate Problems understanding proof of Cauchy theorem
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Undergrad Zero eigenvalues or eigenvectors
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Graduate Need help understanding splitting fields
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Undergrad Can anyone give an intuitive proof of the theorem on polynomial factorization?
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MHB Reflection Matrices: Find Components of R
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Graduate Scalar triple product and abstract vector space
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MHB Convert infinite solution to vector form
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MHB What Are the Basic Properties of This Lie Algebra?
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Undergrad Simple explanation of group generators
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MHB SU(2) and elementary properites of Lie Algebras
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MHB Issue 2 - Tapp - Characterizations of the Orthogonal Groups
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MHB Characterizations of the Orthogonal Groups _ Tapp, Ch. 3, Section 2
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Graduate Solving for P_x(X) given P_y(Y) and P_(x+y)(X+Y)
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High School Can you solve this system of simultaneous equations?
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Graduate Algorithm to find square root of a quadratic residue mod p
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MHB Rotations, Complex Matrices and Real Matrices - Proof of Tapp, Proposition 2.2
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MHB Rotations, Complex Matrices and Real Matrices
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Graduate A question about derived functors
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Undergrad Applying rules to simplify a 3 x 3 determinant
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Undergrad I need to transpose for the value of Q
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Graduate Algebraic Closure: Finite Fields & Equivalent Statements
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Graduate Have you done PA=LU factorization?
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Graduate Components of adjoint representations
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Graduate No cycles in permutation N how to calculate sgn(N^2)?
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MHB Does Property (2) Imply Property (1) for Unit Quaternions?
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MHB Is a Shifted Solution Still Valid?
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Graduate Definition of unconnected subgroups
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Undergrad How Do You Calculate the Square of a Permutation Matrix?
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MHB What is the purpose of computing the transpose of a matrix?
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Undergrad Confused about vectors and transformations (linear)
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Graduate Maximal ideal not containing specific expression
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Graduate Euclidean space: dot product and orthonormal basis
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Graduate Not understanding the isomorphism R x R = C
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MHB Order of Operations for Matrices in Scientific Computing
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MHB Parametric equations and augmented coefficient matrices
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Undergrad Row/column operation on matrices and determinants
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Graduate Adjoint and inverse of product of operators
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Graduate Understanding Aut(Aut(Aut(C_73))) in Group Theory
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Graduate How can the Sherman-Morrison formula simplify matrix inversion?
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MHB Linearly Independent: Why ${}\left\{X+Y, Y+Z, Z+W, W+X\right\}$ Isn't
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Graduate When is integral closure generated by one element
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MHB Understanding a problem in ring theory
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Graduate Unique factorization over fields/rings
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Undergrad Image of a Matrix and symmetric matrix
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MHB Calculation of the commutator of the hamiltonian and position
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Graduate Riemann's zeta function fractal because of Voronin?
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Graduate Vector multiply that is NOT dot or cross?
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Undergrad Question on solving linear recurrence relations
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Graduate Why there's no L^2[-inf,inf] space?
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Undergrad How can I solve a system of equations with two unknowns?
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Graduate Which is the space of mappings from L^2 to itself?
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Undergrad How does L from LU give us column space?
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MHB Lower Central Series: Meaning of Gamma of G
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Graduate Question on group theory: simplest math construction
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Graduate Complex Representations: Real vs. Complex Lie Algebras
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Graduate Linearity in the Vector triple product
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MHB Simple Grammar Problem: Is "a" or "the" Ideal in Lie Algebra?
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Undergrad Intuition & use of M*M^T product of matrix & its transpose?
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MHB Range and Image of a Transformation
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Graduate Basic transcendental field extension question
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Graduate Understanding Scalar Triple Product (STP)
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MHB Violation of Linear Transformation?
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Graduate Understanding Basis Change with Hamiltonian Matrices
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MHB Proof of Conjugate Cycles Property of Permutations
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MHB Ideals of formal power series ring
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MHB Transformation of a Parallelogram
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MHB Linear Transformation of a Plane
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MHB Sketch of the Reflection Transformation of a Parallelogram
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Undergrad How Do You Simplify This Vector Expression?
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Graduate Calculating angle of circle to produce given ellipse
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MHB Show that a Parametric Equation Maps To Another Line By Linear Transformation.
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Undergrad Prove to myself that rotation is a linear transformation?
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Graduate Do Gramian Matrices Have Only One Non-Zero Eigenvalue?
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Graduate Help finding a topic in Number Theory
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Undergrad Determine if all vectors of form (a,0,0) are subspace of R3
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Undergrad Gaussian elimination: Proof of correctness
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MHB Is $f(x) = mx + b$ a Linear Transformation?
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Graduate Understanding the fundamental theorem of algebra
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Graduate Why is the core of a subgroup contained in the subgroup?
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Graduate Properties, General Results on of Aut(G) ?
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MHB Solving (A+B)^-1: Is A^-1+ B^-1 the Answer?
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MHB How Do You Prove Two Spans Are Equal?
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Graduate Does an operation have to be closed?
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Graduate Eigenvalues/vectors of Hermitian and corresponding unitary
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MHB Extending Vectors to a Basis of R^4: Why Notation Matters
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Undergrad Graphing Functions in n Dimensions, Parametric Equations
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MHB Is \( U \) a Subspace of \( F[0,1] \)?
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Graduate Why do the conjugate classes of a group partition the group?
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Undergrad Rotation matrix multiplied by matrix of column vectors?
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Graduate Why Is the Index Shifted in Laplacian Eigenvalues?
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MHB Is My Matrix Solution Correct?
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Graduate Adjoint of an adjoint of a linear map
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Graduate Can Vectors Span Just the Unit Sphere in Spherical Geometry?
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Graduate Rubik's cube group element with the smallest order
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MHB How to Solve a System of Three Equations with Three Unknowns?
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MHB Proving Subspace: Basic Proof for $V(A)$
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Graduate Why is ##Aut(C_8)## not a cyclic group?
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