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.
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MHB Linear Algebra Proofs and Problems
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I About the existence of Hamel basis for vector spaces
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A The colorful world of ##2\times 2## complex matrices
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I When are Markov Matrices also Martingales?
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I Derivation of equations of stress tensor transformation
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I Determine whether ##125## is a unit in ##\mathbb{Z_471}##
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I Trouble understanding an online solution to an exercise in Dummit & Foote
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I Trouble with a passage in Zariski & Samuel's Commutative algebra text
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I Determining isomorphism for ##\frac{R}{(a, b)}##
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I Differences between left vs right actions in some group theory questions
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A Decomposition into irreps of compact Lie group
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I Questions about non existence of GCDs vs (coimages, cokernels)
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I Question about "A Group Epimorphism is Surjective"
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I Localising a non integral domain at a prime
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I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?
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I Meaning of ##\coprod_{x\in\mathrm{Spec}R}R/\mathfrak{p}_x##
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Insights Groups, The Path from a Simple Concept to Mysterious Results
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I Can one find a matrix that's 'unique' to a collection of eigenvectors?
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I Dfns group action & group, written in terms of the other
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I Clarifications needed for an exercise in Hungerford's abstract algebra
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A Have I solved this iterative equation correctly?
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I Equivalent definitons for primitive polynomials
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I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional
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I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
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I Localizing single variable quotient polynomial ring at a prime ideal
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I Make a list of all irreducible polynomials of degrees 1 to 5 over F2
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I ##S_{n}(\alpha)=\sum_{k=1}^{n} (-1)^{\lfloor{k\alpha\rfloor}}##
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I Meaning of the notations: ##\mathbb{Z}[\frac{1}{a}]##
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I How do we distinguish two different notations for cokernel and coimage?
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A linear programming, polyhedron and extreme points
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I Definition of minimal ideal using symbolic logic notation
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I Meaning of "identify" & variations in different math context
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I Meaning of "passage to the quotient"?
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I Correct constructed example of Abelian Monoid?
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I Notation questions about kernel, cokernel, image and coimage
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I Proof of ##\cap_{i\in \cup F}A_i=\cap_{x\in F}(\cap_{i\in X}A_i)##?
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I Correct state row entries in the following Sequential machine?
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I A true or false statement concerning condition number of a matrix
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I Proving inequality about dimension of quotient vector spaces
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A Displacement-Rotation Algorithm
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I Symbol for matrix representative of a tensor
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A Near-Rings with Noncommutative Addition and Two-Sided Distributivity
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I Proof by induction of block diagonal decomposition of a matrix
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B Higher Dimensional Vectors
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B The Relationship Between Function and Ordering Relation
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I How does this binomial expand?
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I Solving matrix commutator equations?
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I Wronskian: null space equals the span of independent functions
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I Uniqueness of reduced row echelon form (proof verification)
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A Question about ##FG## modules
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I ##\mathbb{C}\oplus\mathbb{C}\cong\mathbb{C}\otimes\mathbb{C}##
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I Confused about small detail in rank-nullity theorem
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I Characterizing linear independence in terms of span
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I bra-ket with adjoints identity
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I Matrix rank in terms of determinant polynomial
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A Deduce that the spectrum of a local ring is always connected
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I Is the Cauchy stress tensor really a tensor?
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A Lectures by Richard Borcherds
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I Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
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I Use of induction in the proof of the Chinese Remainder Theorem
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I Orthogonal transformations preserve length
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I "Easy example" of transcendental numbers
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I Mapping tensor products into a Clifford algebra
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I Composite quantum systems: Kronecker and Hadamard/Schur products
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I Use of Laplacian operator in Operations Research Book
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I Index notation of vector rotation
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A A part in a solution for exercise 1.24 from Atiyah-MacDonald
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I Jacobi matrix diagonalization problems
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B Subspaces of Functions- definition
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I Uniform convergence and pointwise convergence
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I What does V^G mean in linear algebra?
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I Seeking an intuition linking definitions of contravariant and covariant
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I Understanding the ##ε## as used in limits of sequences
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I Generators of translations
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I Did I figure-out z-translation of 2D-coordinates correctly?
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I Fundamental theorem of arithmetic from Jordan-Hölder theorem
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I The Lie algebra of ##\frak{so}(3)## without complexification
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I Applying change of basis to vector b_1 doesn't give b'_1?
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A What Is the Role of 'n' and the Virgule in the Wedge Product Formalism?
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I Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
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I Is a 1x1 Matrix Considered a Scalar in Mathematics?
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I Convergence and divergence of series and sequences
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I In 4x4 matrix when does row swapping not affect eigenvaluess?
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A The meaning of ##(ict, x_1,x_2,x_3)##
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A Hidden symmetries in subgroups of Lie groups?
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I The Orthogonality of the Eigenvectors of a 2x2 Hermitian Matrix
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A The original definition of Category
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A Why are the eigenvectors of this hermitian matrix not orthogonal?
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I Equivalence of 2 definitions of the magnitude of the cross product?
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I Matrix diagonalization algorithm
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A Can anybody please explain in layman terms the super-vector spaces?
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I Dimension of a vector space and its subspaces
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I How does one find the dual of a matrix?
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I Definition of the special unitary group
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A Can three elbows generate any point in space?
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I Passive Transformation and Rotation Matrix
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I How can the dual tensors derivation be achieved using rotation matrices?
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I Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction
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I Unravelling Structure of a Symmetric Matrix
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I Question about vector spaces and subsets
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B What unique contributions to math did linear algebra make?
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