Linear and Abstract Algebra Forum

Post thread
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.
  • Sticky
MHB Linear Algebra Proofs and Problems
  • · Replies 1 ·
Replies
1
Views
24K
Graduate Confusion about the Moyal-Weyl twist
  • · Replies 4 ·
Replies
4
Views
465
Undergrad How to define a vector field?
  • · Replies 23 ·
Replies
23
Views
3K
Graduate The colorful world of ##2\times 2## complex matrices
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad About the existence of Hamel basis for vector spaces
  • · Replies 32 ·
2
Replies
32
Views
4K
Undergrad When are Markov Matrices also Martingales?
  • · Replies 5 ·
Replies
5
Views
653
Undergrad Derivation of equations of stress tensor transformation
  • · Replies 2 ·
Replies
2
Views
791
Undergrad Determine whether ##125## is a unit in ##\mathbb{Z_471}##
  • · Replies 3 ·
Replies
3
Views
620
Undergrad Trouble understanding an online solution to an exercise in Dummit & Foote
  • · Replies 21 ·
Replies
21
Views
1K
Undergrad Trouble with a passage in Zariski & Samuel's Commutative algebra text
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Determining isomorphism for ##\frac{R}{(a, b)}##
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Differences between left vs right actions in some group theory questions
  • · Replies 1 ·
Replies
1
Views
530
Graduate Decomposition into irreps of compact Lie group
  • · Replies 4 ·
Replies
4
Views
525
Undergrad Questions about non existence of GCDs vs (coimages, cokernels)
  • · Replies 12 ·
Replies
12
Views
610
Undergrad Question about "A Group Epimorphism is Surjective"
  • · Replies 13 ·
Replies
13
Views
1K
Undergrad Localising a non integral domain at a prime
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?
  • · Replies 31 ·
2
Replies
31
Views
2K
Undergrad Meaning of ##\coprod_{x\in\mathrm{Spec}R}R/\mathfrak{p}_x##
  • · Replies 11 ·
Replies
11
Views
1K
Insights Groups, The Path from a Simple Concept to Mysterious Results
  • · Replies 17 ·
Replies
17
Views
9K
Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
2K
Undergrad Dfns group action & group, written in terms of the other
  • · Replies 26 ·
Replies
26
Views
852
Undergrad Clarifications needed for an exercise in Hungerford's abstract algebra
  • · Replies 23 ·
Replies
23
Views
949
Graduate Have I solved this iterative equation correctly?
  • · Replies 2 ·
Replies
2
Views
648
Undergrad Equivalent definitons for primitive polynomials
  • · Replies 24 ·
Replies
24
Views
871
Undergrad Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional
  • · Replies 40 ·
2
Replies
40
Views
3K
Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
  • · Replies 48 ·
2
Replies
48
Views
4K
Undergrad Localizing single variable quotient polynomial ring at a prime ideal
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Make a list of all irreducible polynomials of degrees 1 to 5 over F2
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad ##S_{n}(\alpha)=\sum_{k=1}^{n} (-1)^{\lfloor{k\alpha\rfloor}}##
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Meaning of the notations: ##\mathbb{Z}[\frac{1}{a}]##
  • · Replies 1 ·
Replies
1
Views
863
Undergrad How do we distinguish two different notations for cokernel and coimage?
  • · Replies 41 ·
2
Replies
41
Views
2K
Graduate linear programming, polyhedron and extreme points
  • · Replies 3 ·
Replies
3
Views
936
Undergrad Definition of minimal ideal using symbolic logic notation
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Meaning of "identify" & variations in different math context
  • · Replies 5 ·
Replies
5
Views
939
Undergrad Meaning of "passage to the quotient"?
  • · Replies 3 ·
Replies
3
Views
877
Undergrad Correct constructed example of Abelian Monoid?
  • · Replies 0 ·
Replies
0
Views
839
Undergrad Notation questions about kernel, cokernel, image and coimage
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Proof of ##\cap_{i\in \cup F}A_i=\cap_{x\in F}(\cap_{i\in X}A_i)##?
  • · Replies 3 ·
Replies
3
Views
969
Undergrad Correct state row entries in the following Sequential machine?
  • · Replies 0 ·
Replies
0
Views
842
Undergrad A true or false statement concerning condition number of a matrix
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Proving inequality about dimension of quotient vector spaces
  • · Replies 25 ·
Replies
25
Views
3K
Graduate Displacement-Rotation Algorithm
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Symbol for matrix representative of a tensor
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Near-Rings with Noncommutative Addition and Two-Sided Distributivity
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Proof by induction of block diagonal decomposition of a matrix
  • · Replies 4 ·
Replies
4
Views
2K
High School Higher Dimensional Vectors
  • · Replies 5 ·
Replies
5
Views
1K
High School The Relationship Between Function and Ordering Relation
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad How does this binomial expand?
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Solving matrix commutator equations?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Wronskian: null space equals the span of independent functions
  • · Replies 23 ·
Replies
23
Views
2K
Undergrad Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Question about ##FG## modules
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad ##\mathbb{C}\oplus\mathbb{C}\cong\mathbb{C}\otimes\mathbb{C}##
  • · Replies 14 ·
Replies
14
Views
5K
Undergrad Confused about small detail in rank-nullity theorem
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Characterizing linear independence in terms of span
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad bra-ket with adjoints identity
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
3K
Graduate Deduce that the spectrum of a local ring is always connected
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Is the Cauchy stress tensor really a tensor?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Lectures by Richard Borcherds
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Use of induction in the proof of the Chinese Remainder Theorem
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Orthogonal transformations preserve length
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad "Easy example" of transcendental numbers
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Mapping tensor products into a Clifford algebra
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Composite quantum systems: Kronecker and Hadamard/Schur products
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Use of Laplacian operator in Operations Research Book
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Index notation of vector rotation
  • · Replies 7 ·
Replies
7
Views
2K
Graduate A part in a solution for exercise 1.24 from Atiyah-MacDonald
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Jacobi matrix diagonalization problems
  • · Replies 5 ·
Replies
5
Views
2K
High School Subspaces of Functions- definition
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Uniform convergence and pointwise convergence
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad What does V^G mean in linear algebra?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Seeking an intuition linking definitions of contravariant and covariant
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Understanding the ##ε## as used in limits of sequences
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Generators of translations
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Did I figure-out z-translation of 2D-coordinates correctly?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad The Lie algebra of ##\frak{so}(3)## without complexification
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Applying change of basis to vector b_1 doesn't give b'_1?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate What Is the Role of 'n' and the Virgule in the Wedge Product Formalism?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Calculating Pitch and Roll Relative to a Velocity Vector from IMU Data
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Is a 1x1 Matrix Considered a Scalar in Mathematics?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad Convergence and divergence of series and sequences
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad In 4x4 matrix when does row swapping not affect eigenvaluess?
  • · Replies 6 ·
Replies
6
Views
4K
Graduate The meaning of ##(ict, x_1,x_2,x_3)##
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Hidden symmetries in subgroups of Lie groups?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad The Orthogonality of the Eigenvectors of a 2x2 Hermitian Matrix
  • · Replies 13 ·
Replies
13
Views
3K
Graduate The original definition of Category
  • · Replies 45 ·
2
Replies
45
Views
5K
Graduate Why are the eigenvectors of this hermitian matrix not orthogonal?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Equivalence of 2 definitions of the magnitude of the cross product?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Matrix diagonalization algorithm
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Can anybody please explain in layman terms the super-vector spaces?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Dimension of a vector space and its subspaces
  • · Replies 15 ·
Replies
15
Views
4K
Undergrad How does one find the dual of a matrix?
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Definition of the special unitary group
  • · Replies 46 ·
2
Replies
46
Views
6K
Graduate Can three elbows generate any point in space?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Passive Transformation and Rotation Matrix
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How can the dual tensors derivation be achieved using rotation matrices?
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad Prove Even # Transpositions in Identity Permutation w/ Induction & Contradiction
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad Unravelling Structure of a Symmetric Matrix
  • · Replies 5 ·
Replies
5
Views
3K