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