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.
Undergrad Transformation matrix, vector algebra word problem
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Grander than the Riemann Hypothesis
  • · Replies 9 ·
Replies
9
Views
4K
Graduate On the invertibility of symmetric Toeplitz matrices
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Answer: Lie Algebras: Adjoint Representations of Same Dimension as Basis
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Quandles are associated with knot theory
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad How can you determine if a set of given vectors can span a subspace in R^n?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Clock Design for Zeta Zeros Mechanic Calculator
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad What Does a 2x2 Matrix Represent in Vector Spaces?
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Can [F: F ∩ E] Differ from 2 in Quadratic Field Extensions?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Points on an unit circle over finite field
  • · Replies 2 ·
Replies
2
Views
6K
Undergrad Symmetric Matrices to Jordan Blocks
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Matrix pseudo-inverse to do inverse discrete fourier transform
  • · Replies 3 ·
Replies
3
Views
9K
Graduate Example of Kronecker Delta Identity in 3D Matrix R
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Proving ab|c: The Proof for (a,b)=1
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why Do the Determinants of a Matrix and Its Transpose Equal?
  • · Replies 12 ·
Replies
12
Views
25K
Graduate Is Every Ideal in a Ring the Kernel of a Homomorphism?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Do Linear Space Properties Ever Fail in the Real and Complex Planes?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Eigenvalues - real and imaginary
  • · Replies 1 ·
Replies
1
Views
6K
Graduate Constructing Isomorphisms for D4 and A4
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Number of groups of a given order?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Question about Lie Brackets in Group Theory
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad How can a determinant of a matrix become an area?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Converting rational number to a new base.
  • · Replies 6 ·
Replies
6
Views
8K
Undergrad Determinant of a non square matrix
  • · Replies 2 ·
Replies
2
Views
7K
Undergrad Understanding Exterior Algebra: Determinant from Wedge Product
  • · Replies 3 ·
Replies
3
Views
8K
Graduate Dashed arrow and solid arrow in category theory
  • · Replies 7 ·
Replies
7
Views
13K
Undergrad Localization of Z: Understand What It Is
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Need to find eigenvector that corresponds to max eigenvalue
  • · Replies 2 ·
Replies
2
Views
7K
Undergrad Trace of a matrix equals sum of its determinants?
  • · Replies 2 ·
Replies
2
Views
8K
Graduate Can a Basis for a Subspace Always Include Specific Elements of a Larger Basis?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Dot product between Spherical and Rectangular.
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Homomorphism from Z into a nonabelian group
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Studying Geometric Algebra: Degenerate & Nondegenerate Forms Explained
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Flaw in 3D Vector Definition: Solving for t and x Step by Step
  • · Replies 14 ·
Replies
14
Views
4K
Graduate Laplace transform as a dual space
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Solving Complex Equations with x, y, z
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Vector subspace as the space of solutions to matrix multiplication
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is the transitivity of the complex orthogonal group on generalized spheres?
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Matrix S^n: Generalizing Matrix Operations
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad What the equivalence class suppose to be
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Why Do O(V) and SO(V) Have the Same Lie Algebra?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Proving transpose(AB)=transpose(B)*tranpose(A) Help Needed
  • · Replies 9 ·
Replies
9
Views
18K
Graduate Is there a version of Jordan-Hölder theorem for infinite composition series?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Hubbard's & Hubbards Concrete To Abstract Function
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Difficult Question on Permutations
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Viewing Polynomials from k[x,y] as Elements of k[y][x]
  • · Replies 4 ·
Replies
4
Views
3K
High School I'm already clueless about simple algebra word problems. Dreams = *POOF*
  • · Replies 11 ·
Replies
11
Views
3K
Graduate Is Rank(TS) Always Less Than or Equal to Rank(T)?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Linear independence and orthogonaliy
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Solve Rotation Matrices w/ X, Y, Z Axes
  • · Replies 6 ·
Replies
6
Views
5K
Graduate Adjoint representation/lie algebra question
  • · Replies 21 ·
Replies
21
Views
11K
Graduate Fermats little theorem on permutations
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Rot Matrix for nxn: Group of Rotations
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Dimension of U,V and W over K: Do they Equal?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Trace and Determinant Relationship: Proving the Relation with O(x^2)
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad Understanding Matrix Dimensions: Calculating Entries and Recognizing Symmetry
  • · Replies 8 ·
Replies
8
Views
123K
Graduate Matrix Exponential Theorem: Proving Formally with Cayley-Hamilton
  • · Replies 3 ·
Replies
3
Views
10K
Graduate Is {x+y(cuberoot of 3) + z(cuberoot of 9) | x,y,z is in Q} a Subfield?
  • · Replies 14 ·
Replies
14
Views
5K
High School Explain an Orbit: Simple Definition & Example
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Factorization of Polynomials over a field
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Fast primality test for small numbers
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Minimal Invariant Subspaces: The Role of Orthogonal Linear Transformations
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Is 550 the Correct Remainder for the Sum of the Series in Modular Arithmetic?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate What is the relationship between p-adic and l-adic numbers?
  • · Replies 7 ·
Replies
7
Views
6K
Undergrad Understanding the Addition of Subspaces in Linear Algebra
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Challeng in simplifying the Grammer
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why is M Torsion-free & Rank 1 but Not a Free R-Module?
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Where Can I Find Resources for Learning Linear and Abstract Algebra?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Are Relatively Prime Numbers Always Coprime?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad A Visual Representation of the Vector Scalar Product?
  • · Replies 5 ·
Replies
5
Views
8K
High School How many fish were originally caught by Mr X in total?
  • · Replies 1 ·
Replies
1
Views
3K
High School Rule of Division by 23: What is it?
  • · Replies 20 ·
Replies
20
Views
5K
Undergrad Matrix multiplication: Communicative property.
  • · Replies 10 ·
Replies
10
Views
16K
Graduate How Are Lagrange Polynomials Computed and Proven?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Complex Zeros in Riemann Zeta Function: Is it Possible?
  • · Replies 31 ·
2
Replies
31
Views
7K
Undergrad Does commutativity imply associativity?
  • · Replies 5 ·
Replies
5
Views
6K
Graduate What Are the Key Questions About Inner Product Spaces?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate How can I prove the Riesz representation theorem?
  • · Replies 12 ·
Replies
12
Views
8K
Undergrad Is Abstract Algebra a Necessary Foundation for Mathematical Maturity?
  • · Replies 18 ·
Replies
18
Views
16K
Undergrad Elementary Row Operations - only need two?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Vector multiplication question
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Is there a simple way to determine if an element is a primitive root modulo n?
  • · Replies 4 ·
Replies
4
Views
6K
Undergrad Rows that get zeroed out during elimination
  • · Replies 2 ·
Replies
2
Views
2K
High School Is 0.9999... Equal to 1? Debunking the Myth and Understanding the Concept
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Correspondence between between tensor product and bilinear maps
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Divisor Function t(n): Proving $2n*(n)^{1/2}$
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Linear Dependence Check: [-1, 1]
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Show that Polynomials p0 to pn Form Basis of F[t] ≤ n
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Matrix of a Parabola? (It's my first day)
  • · Replies 5 ·
Replies
5
Views
7K
Undergrad Need help designing a model and using excel
  • · Replies 1 ·
Replies
1
Views
2K
Graduate One-parameter subgroups and exponentials
  • · Replies 4 ·
Replies
4
Views
2K
Graduate What Makes Natural Isomorphisms Important in Vector Spaces?
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Linear transformation and its matrix
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad What Are the Possible Sums of Prime Number Pairs?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Tensor Product of V1 and V2 in Vector Space V: 0 Intersection Required?
  • · Replies 3 ·
Replies
3
Views
3K
High School Core of matrix (pure translatio)
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad What does the 'X' mean in the Mueller matrix rotation equation?
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Proof, intersection and sum of vector spaces
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Apparent fallacy in linear operator theory
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why eigenvalue specification reduces the no. of LI equations?
  • · Replies 1 ·
Replies
1
Views
2K