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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High School Calculation of "momentum" vector's head coordinates
- LucKy
- · Replies 3 ·
Undergrad Uniform convergence and pointwise convergence
- chwala
- · Replies 26 ·
Graduate Is this Hessian/spectral viewpoint known?
- Roberto Pavani
- · Replies 8 ·
Undergrad Is the Cauchy stress tensor really a tensor?
- Philip Wood
- · Replies 11 ·
Graduate Finding dual optimum of a linear problem
- Trollfaz
- · Replies 1 ·
Undergrad Why are these cycles disjoint and of equal length?
- Hill
- · Replies 2 ·
Undergrad Looking for a paper about spinors
- grzz
- · Replies 3 ·
Undergrad Matrix representation of rank-2 spinors
- grzz
- · Replies 2 ·
Undergrad Spinor calculus
- grzz
- · Replies 2 ·
Undergrad The vector to which a dual vector corresponds
- nomadreid
- · Replies 13 ·
On the Moore–Penrose inverse from a banal linear algebra viewpoint
- wrobel
- · Replies 0 ·
Undergrad When to use bra or dual space view of inner products?
- nomadreid
- · Replies 10 ·
Undergrad A typo in the proof of group homomorphism of pairs?
- Hill
- · Replies 1 ·
Graduate Confusion about the Moyal-Weyl twist
- gasgas
- · Replies 4 ·
Undergrad How to define a vector field?
- Mike_bb
- · Replies 23 ·
Undergrad Erroneously finding discrepancy in transpose rule
- nomadreid
- · Replies 13 ·
Graduate The colorful world of ##2\times 2## complex matrices
- mma
- · Replies 22 ·
Undergrad Do vector spaces always have a Hamel basis without the axiom of choice?
- cianfa72
- · Replies 32 ·
Undergrad When are Markov Matrices also Martingales?
- WWGD
- · Replies 5 ·
Undergrad Derivation of equations of stress tensor transformation
- Mike_bb
- · Replies 2 ·
Undergrad Non-orthogonal bases
- geordief
- · Replies 12 ·
Undergrad Determine whether ##125## is a unit in ##\mathbb{Z_471}##
- chwala
- · Replies 3 ·
Undergrad Trouble understanding an online solution to an exercise in Dummit & Foote
- elias001
- · Replies 21 ·
Undergrad Notation for ring homomorphisms in Zariski & Samuel's localization passage
- elias001
- · Replies 5 ·
Undergrad Determining isomorphism for ##\frac{R}{(a, b)}##
- elias001
- · Replies 4 ·
Undergrad Differences between left vs right actions in some group theory questions
- elias001
- · Replies 1 ·
Graduate Decomposition into irreps of compact Lie group
- Orodruin
- · Replies 4 ·
Undergrad Questions about non existence of GCDs vs (coimages, cokernels)
- elias001
- · Replies 12 ·
Undergrad Question about "A Group Epimorphism is Surjective"
- elias001
- · Replies 13 ·
Undergrad Localising a non integral domain at a prime
- elias001
- · Replies 17 ·
Undergrad ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?
- elias001
- · Replies 31 ·
Undergrad Meaning of ##\coprod_{x\in\mathrm{Spec}R}R/\mathfrak{p}_x##
- elias001
- · Replies 11 ·
Insights Groups, The Path from a Simple Concept to Mysterious Results
- fresh_42
- · Replies 17 ·
Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
- Sciencemaster
- · Replies 33 ·
Undergrad Expressing group definitions via group action and vice versa
- elias001
- · Replies 26 ·
Undergrad Proving a divides c when gcd(a,b)=1 in a UFD
- elias001
- · Replies 23 ·
Graduate Have I solved this iterative equation correctly?
- Tygra
- · Replies 2 ·
Undergrad Equivalent definitons for primitive polynomials
- elias001
- · Replies 24 ·
Undergrad Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional
- elias001
- · Replies 40 ·
Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
- elias001
- · Replies 48 ·
Undergrad Localizing single variable quotient polynomial ring at a prime ideal
- elias001
- · Replies 6 ·
Undergrad Make a list of all irreducible polynomials of degrees 1 to 5 over F2
- Hill
- · Replies 4 ·
Undergrad ##S_{n}(\alpha)=\sum_{k=1}^{n} (-1)^{\lfloor{k\alpha\rfloor}}##
- elias001
- · Replies 2 ·
Undergrad Meaning of the notations: ##\mathbb{Z}[\frac{1}{a}]##
- elias001
- · Replies 1 ·
Undergrad How do we distinguish two different notations for cokernel and coimage?
- elias001
- · Replies 41 ·
Graduate linear programming, polyhedron and extreme points
- mertcan
- · Replies 3 ·
Undergrad Definition of minimal ideal using symbolic logic notation
- elias001
- · Replies 3 ·
Undergrad Does 'identify' mean equality or isomorphism in algebra texts?
- elias001
- · Replies 5 ·
Undergrad Meaning of "passage to the quotient"?
- elias001
- · Replies 3 ·
Undergrad Correct constructed example of Abelian Monoid?
- elias001
- · Replies 0 ·
Undergrad Notation questions about kernel, cokernel, image and coimage
- elias001
- · Replies 7 ·
Undergrad Proof of ##\cap_{i\in \cup F}A_i=\cap_{x\in F}(\cap_{i\in X}A_i)##?
- elias001
- · Replies 3 ·
Undergrad Correct state row entries in the following Sequential machine?
- elias001
- · Replies 0 ·
Undergrad A true or false statement concerning condition number of a matrix
- psie
- · Replies 2 ·
Undergrad Proving inequality about dimension of quotient vector spaces
- elias001
- · Replies 25 ·
Graduate Displacement-Rotation Algorithm
- Muhammad
- · Replies 2 ·
Undergrad Symbol for matrix representative of a tensor
- doktorglas
- · Replies 5 ·
Graduate Near-Rings with Noncommutative Addition and Two-Sided Distributivity
- lpetrich
- · Replies 4 ·
Undergrad Proof by induction of block diagonal decomposition of a matrix
- psie
- · Replies 4 ·
High School Higher Dimensional Vectors
- Hornbein
- · Replies 5 ·
High School The Relationship Between Function and Ordering Relation
- littlemathquark
- · Replies 8 ·
Undergrad How does this binomial expand?
- lioric
- · Replies 19 ·
Undergrad Solving matrix commutator equations?
- Filip Larsen
- · Replies 7 ·
Undergrad Proving null space of Wronskian equals span of linearly independent functions
- psie
- · Replies 23 ·
Undergrad Uniqueness of reduced row echelon form (proof verification)
- psie
- · Replies 4 ·
Graduate How does v·f(g) work for an arbitrary FG-module?
- MathLearner123
- · Replies 14 ·
Insights Why Vector Spaces Explain The World: A Historical Perspective
- fresh_42
- · Replies 0 ·
Undergrad ##\mathbb{C}\oplus\mathbb{C}\cong\mathbb{C}\otimes\mathbb{C}##
- Korybut
- · Replies 14 ·
Undergrad Why must T(v_{k+1}),...,T(v_n) be distinct in rank-nullity proof?
- psie
- · Replies 1 ·
Undergrad Characterizing linear independence in terms of span
- psie
- · Replies 3 ·
Undergrad bra-ket with adjoints identity
- nomadreid
- · Replies 3 ·
Undergrad Matrix rank in terms of determinant polynomial
- mupe03
- · Replies 14 ·
Graduate Deduce that the spectrum of a local ring is always connected
- mad mathematician
- · Replies 2 ·
Graduate Lectures by Richard Borcherds
- martinbn
- · Replies 4 ·
High School When are two vectors collinear and coplanar?
- PLAGUE
- · Replies 10 ·
Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
- Hardy
- · Replies 0 ·
Undergrad Use of induction in the proof of the Chinese Remainder Theorem
- Hill
- · Replies 7 ·
Undergrad Orthogonal transformations preserve length
- lys04
- · Replies 1 ·
Undergrad "Easy example" of transcendental numbers
- Hill
- · Replies 9 ·
Undergrad Mapping tensor products into a Clifford algebra
- jv07cs
- · Replies 7 ·
Undergrad Composite quantum systems: Kronecker and Hadamard/Schur products
- Dr_Nate
- · Replies 2 ·
Undergrad Use of Laplacian operator in Operations Research Book
- hotvette
- · Replies 6 ·
Undergrad Index notation of vector rotation
- shinobi20
- · Replies 7 ·
Graduate Why add 2ac+2ab+2abc in distributivity proof from Atiyah-MacDonald 1.24
- mad mathematician
- · Replies 2 ·
Undergrad Jacobi matrix diagonalization problems
- Spathi
- · Replies 5 ·
High School Subspaces of Functions- definition
- sonnichs
- · Replies 8 ·
Undergrad What does V^G mean in linear algebra?
- cask1
- · Replies 3 ·
Undergrad Seeking an intuition linking definitions of contravariant and covariant
- nomadreid
- · Replies 1 ·
Undergrad Finding N for a given ε in the limit definition of sequences
- chwala
- · Replies 2 ·
Undergrad Generators of translations
- redtree
- · Replies 0 ·
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
- william_
- · Replies 4 ·
Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
- eoghan
- · Replies 5 ·
Undergrad The Lie algebra of ##\frak{so}(3)## without complexification
- redtree
- · Replies 2 ·
Undergrad Applying change of basis to vector b_1 doesn't give b'_1?
- giraffe714
- · Replies 8 ·
Graduate What Is the Role of 'n' and the Virgule in the Wedge Product Formalism?
- Bill_1
- · Replies 3 ·
Undergrad Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
- FGD
- · Replies 5 ·
Undergrad Is a 1x1 Matrix Considered a Scalar in Mathematics?
- laser1
- · Replies 12 ·
Graduate Mathematical structures beyond tensors and holors
- billtodd
- · Replies 8 ·
Undergrad Convergence and divergence of series and sequences
- chwala
- · Replies 7 ·
Undergrad In 4x4 matrix when does row swapping not affect eigenvaluess?
- NotEuler
- · Replies 6 ·