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.
Graduate Correct reasoning about direct sums proof?
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Young Tableux and representation theory
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How to compute row-reduced echelon form and understand upper triangular matrices
  • · Replies 7 ·
Replies
7
Views
7K
Undergrad Vector question to think about
  • · Replies 15 ·
Replies
15
Views
4K
Graduate What will I learn in a course on Groups and Symmetries?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Why Adjoint Representation Has a Higher Dimension Than Basis Matrices?
  • · Replies 16 ·
Replies
16
Views
8K
Undergrad Linear independence after change of basis
  • · Replies 2 ·
Replies
2
Views
3K
Graduate What is the kernel of a field morphism and how is it related to ideals?
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Can Monads Transform the User Experience on YouTube?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Construction of a cyclic sequence re the Golden Ratio
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Solving Cross Product w/ Determinants: Setting Up Equations
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad What is the mathematical logic behind scalar and cross product definitions?
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Lie algebra, ideal and isomorphism
  • · Replies 13 ·
Replies
13
Views
5K
Graduate Are Algebraic Closures of a Field Isomorphic?
  • · Replies 22 ·
Replies
22
Views
8K
Undergrad Demonstration/proof advice needed
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Galois Solvable Group and Realizability over \mathbb{Q} for |G|=p^n
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Number Theory: Find Multiplicative Order for (a,n) = 1
  • · Replies 2 ·
Replies
2
Views
4K
High School Number Patterns and Multiples of 9: Investigating Interesting Sequences from 2-9
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Irreducibility test for polynomials over Fp
  • · Replies 4 ·
Replies
4
Views
6K
Undergrad Crash course in abstract algebra
  • · Replies 19 ·
Replies
19
Views
9K
Graduate Understanding the Trivial Zeros of the Riemann Hypothesis
  • · Replies 9 ·
Replies
9
Views
5K
High School Guessing Number-Generating Algorithm
  • · Replies 6 ·
Replies
6
Views
6K
Graduate What's the effect of using modular counting in matrices?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Fermat's Last Theorem: Proving the Impossibility of Integral Solutions for n>2
  • · Replies 52 ·
2
Replies
52
Views
13K
Graduate Group Formation: Converting Sets into Groups with Binary Operations
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Repost of Carrying and cocycles by james dolan (part one)
  • · Replies 2 ·
Replies
2
Views
7K
Undergrad Why are vector spaces and sub-spaces so crucial in math?
  • · Replies 4 ·
Replies
4
Views
5K
Graduate Can the Triangular Number Identity Be Simplified Further for Different Series?
  • · Replies 17 ·
Replies
17
Views
5K
Graduate Gram–Schmidt Process for Orthonormalizing Vectors in R^n
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Solve Fermat's Equation: Leopold Kronecker UFD
  • · Replies 14 ·
Replies
14
Views
5K
High School Orthogonal Matrices Explained: Examples & More
  • · Replies 7 ·
Replies
7
Views
6K
Graduate 'Pseudocubality' - fast tests for large possible-cubes
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad What Are Inverse Transformations and Generating Functions?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Is x²-y²+3xy-x⁴+5y⁴+z⁴-2t⁴+3xyzt-6x²tz+5x²y² a 4-Linear Form?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Hypermatrices and Hyperdeterminant
  • · Replies 6 ·
Replies
6
Views
6K
Graduate Need help to proof Adjugate Matrix
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Question on a form of the Euler constant
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Grassmann Numbers: Generator Symbols & More
  • · Replies 1 ·
Replies
1
Views
11K
Graduate Complementary slackness and the transportation problem
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Non-Inner Product Metric Space: Understanding & Examples
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Understanding the field structure for A_5 and more
  • · Replies 20 ·
Replies
20
Views
6K
Graduate Which Book Explains Linear Operators in Quantum Mechanics for Beginners?
  • · Replies 4 ·
Replies
4
Views
6K
Graduate What is the connection between discriminants and Galois groups?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Proving Constant Sequence of Positive Integers Starting with n
  • · Replies 10 ·
Replies
10
Views
4K
Graduate Prep for Algebra Comprehensive Exam #4
  • · Replies 18 ·
Replies
18
Views
4K
Graduate Discriminant - Nice thinking stump
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Let E be an algebraic over F, F is perfect. Show that E is perfect
  • · Replies 5 ·
Replies
5
Views
4K
Graduate An elementary question regarding Galois theory
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Constructing a Division Ring of Quaternions over K: Conditions and Solutions
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Group isomorphism and Polynomial ring modulo ideal
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Subspace Addition: Understanding the Union of A and B
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Unique Factorization in $\mathbb{Z}[\zeta]$
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Certain product sequences and their factors
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Representations of SU(2) are equivalent to their duals
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Prove Finite Simple Group has no Subgroup of Index 5
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Prep for Algebra Comprehensive Exam #3
  • · Replies 12 ·
Replies
12
Views
4K
Graduate Field trace and norm (Equivalence between definitions)
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Inner Product Space over Fnite Field
  • · Replies 7 ·
Replies
7
Views
6K
Graduate Explaining SO(3) and U(2) Lie Group Relationships to Non-Experts
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Galois extension of a field with Characteristic 0
  • · Replies 1 ·
Replies
1
Views
3K
Graduate What is the pattern of twin prime acceleration?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Why is \(\phi^{-1}(a'b') = (\phi^{-1}a')(\phi^{-1}b')\) True?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Why is x not invertible in F[x]?
  • · Replies 8 ·
Replies
8
Views
10K
Undergrad Understanding Subgroups of Integers: Explained Simply
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Showing that a subgroup is subnormal in the original group G
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Galois Theory (degree 4 polynomial)
  • · Replies 7 ·
Replies
7
Views
5K
Graduate An ideal in a ring as 'analogous' to a normal subgroup of a group, but
  • · Replies 7 ·
Replies
7
Views
7K
High School Free Number Theory Basics for Beginners
  • · Replies 12 ·
Replies
12
Views
8K
Undergrad Solving Linear Program (P): Adding Slack Variables
  • · Replies 2 ·
Replies
2
Views
5K
Graduate It shows that V is the dual space of V*?
  • · Replies 5 ·
Replies
5
Views
4K
Undergrad How do I perform eigenvalue analysis for a matrix without mathematical software?
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Prep for Algebra Comprehensive Exam #2
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Why Does G Equal N_G(P)N in Group Theory?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Solve formulas containing the floor function
  • · Replies 10 ·
Replies
10
Views
7K
Graduate Is G_nm Isomorphic to G_n x G_m?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Cartesian Tensors and transformation matrix
  • · Replies 3 ·
Replies
3
Views
7K
Graduate What is the Orthogonal Decomposition of x from b in terms of RowA and NulA?
  • · Replies 2 ·
Replies
2
Views
6K
Undergrad Linear Algebra Book Recommendations
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Can All Coefficients in a Continued Fraction Be the Same Integer?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Double check - this is prime, yes?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Calculating Eigen Values of a Sparse Matrix
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Prep for Algebra Comprehensive Exam #1
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Function vs mapping vs transformation
  • · Replies 2 ·
Replies
2
Views
12K
Undergrad Determinant Relationship: det(A) and det(-A) for n x n Matrices
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Property of the adjoint operator
  • · Replies 6 ·
Replies
6
Views
8K
Undergrad Is the third condition necessary for a vector space to be considered a subspace?
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Solutions of system of nonlinear equations
  • · Replies 14 ·
Replies
14
Views
8K
Graduate The sum over primes involving powers of 10
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Solving Groups: Proving AB is Solvable w/ A Normal in G
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Can You Construct an Infinite Lattice with Each Integer Exactly Once?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Regarding Orthogonal Transformations
  • · Replies 11 ·
Replies
11
Views
8K
Graduate About invertible and diagonalizable matrices
  • · Replies 4 ·
Replies
4
Views
7K
Undergrad Which text? Second course in linear algebra
  • · Replies 14 ·
Replies
14
Views
8K
Graduate A conjecture on Cesaro summation and primes.
  • · Replies 6 ·
Replies
6
Views
5K
Graduate How Do You Solve Norm and Matrix Approximation Problems in Linear Algebra?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Optimizing Linear Least Squares with Multiple Unknowns: A Partitioned Approach
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Angle preserving linear transformations
  • · Replies 1 ·
Replies
1
Views
5K
Graduate How Do Eigenvalues Relate to Polynomial Roots in Linear Algebra?
  • · Replies 2 ·
Replies
2
Views
3K
High School Solving for the Determinent of a Matrix
  • · Replies 16 ·
Replies
16
Views
68K
Graduate Given an algebraic alpha be of degree n over F, show at most. .
  • · Replies 2 ·
Replies
2
Views
4K