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.
Understand Linear Algebra: Im(BF) in Im(B)?
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Difference between REF/RREF (Gauss vs Gauss-Jordan)?
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MHB Barycentric coordinates in a triangle - proof
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Coefficients on the p-adic expansions
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P-adic norm, valuation, and expansion
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Uncovering Surprising Properties of the Cholesky Decomposition
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How to Simplify a Double Dot Product of Tensors?
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Constructing a field of 4 elements
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Su(2), so(3) and their representations
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QR Decomposition w/ Householder and Givens Transformations
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Double Dot Product: Solving 3D Vector Problem
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Green's Function - modified operator
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Matrices and systems of equations
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What are some real-world applications of cyclic groups and Galois fields?
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Struggling to understand a field theorm's corollary
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Every field contains a copy of Z_p
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MHB Find a Basis for U with $\text{rref}(A)$
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Trouble understanding simple Galois Theory example
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MHB A Basic Question Regarding the Universal Property of the Tensor Product.
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Alternate expression for definition of an Ideal?
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Structure of a Matrix With Empty Null Space
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Problems understanding proof of Cauchy theorem
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Zero eigenvalues or eigenvectors
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Need help understanding splitting fields
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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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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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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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Solving for P_x(X) given P_y(Y) and P_(x+y)(X+Y)
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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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A question about derived functors
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I need to transpose for the value of Q
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Algebraic Closure: Finite Fields & Equivalent Statements
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Have you done PA=LU factorization?
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Components of adjoint representations
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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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Definition of unconnected subgroups
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How Do You Calculate the Square of a Permutation Matrix?
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Confused about vectors and transformations (linear)
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Maximal ideal not containing specific expression
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Euclidean space: dot product and orthonormal basis
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Not understanding the isomorphism R x R = C
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MHB Parametric equations and augmented coefficient matrices
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Row/column operation on matrices and determinants
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Adjoint and inverse of product of operators
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Understanding Aut(Aut(Aut(C_73))) in Group Theory
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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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When is integral closure generated by one element
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MHB Understanding a problem in ring theory
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Unique factorization over fields/rings
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Image of a Matrix and symmetric matrix
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Riemann's zeta function fractal because of Voronin?
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Vector multiply that is NOT dot or cross?
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Why there's no L^2[-inf,inf] space?
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Which is the space of mappings from L^2 to itself?
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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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Question on group theory: simplest math construction
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MHB Simple Grammar Problem: Is "a" or "the" Ideal in Lie Algebra?
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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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Basic transcendental field extension question
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MHB Violation of Linear Transformation?
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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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How Do You Simplify This Vector Expression?
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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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Help finding a topic in Number Theory
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Determine if all vectors of form (a,0,0) are subspace of R3
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Gaussian elimination: Proof of correctness
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MHB Is $f(x) = mx + b$ a Linear Transformation?
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Understanding the fundamental theorem of algebra
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Why is the core of a subgroup contained in the subgroup?
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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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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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MHB Is \( U \) a Subspace of \( F[0,1] \)?
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Why do the conjugate classes of a group partition the group?
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Rotation matrix multiplied by matrix of column vectors?
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Why Is the Index Shifted in Laplacian Eigenvalues?
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MHB Is My Matrix Solution Correct?
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Adjoint of an adjoint of a linear map
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Can Vectors Span Just the Unit Sphere in Spherical Geometry?
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Rubik's cube group element with the smallest order
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