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 Adding a constant times the unit matrix and eigenvalues
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Good method for checking solutions to linear systems of equations by hand
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Coefficients of the characteristic equation
  • · Replies 3 ·
Replies
3
Views
3K
Graduate How to solve a system of linear inequalities with absolute magnitudes?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad AP vs. CPAP: Which is Best for Sleep Apnea?
  • · Replies 5 ·
Replies
5
Views
7K
Graduate Is (2X,5) Really an Ideal in Z[X]?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Difference between product and pullback
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Discover the Pattern of PDS Numbers and Find the Nth PDS Number
  • · Replies 2 ·
Replies
2
Views
4K
MHB System of Equations: (2x-1)(2y-1)
  • · Replies 1 ·
Replies
1
Views
2K
High School What is a nonconstant linear function?
  • · Replies 10 ·
Replies
10
Views
15K
Graduate Is Every Norm on a Finite-Dimensional Vector Space Induced by an Inner Product?
  • · Replies 3 ·
Replies
3
Views
5K
Graduate How to find subgroup of index n in a given group
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Solbing equation A(u)=B(v) for square matrices A and B
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Ring Homomorphism - showing Multiplicativity
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Proof about a prime between k and 2k.
  • · Replies 6 ·
Replies
6
Views
5K
Undergrad Can Solving n = x (mod 10x+1) Simplify Factoring Numbers?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is the Set {cos x, cos 2x, cos 3x, ...} Orthogonal Using Integral Products?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate What is the latest on the Group Extension Problem?
  • · Replies 7 ·
Replies
7
Views
6K
MHB Linear independence of polynomial set.
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Efficient Anti-Triangular Matrix Multiplications
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad How Does the Variable x Relate to n in This Divisibility Problem?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Is Physical Symmetry Limited Due To The Classification Theorem?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Optimizing Bi-Linear Objective Function for Vector Fitting in Flat Space
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Question about Multiplying Matrices
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is 2Z isomorphic to 4Z? (Abstract algebra)
  • · Replies 3 ·
Replies
3
Views
6K
MHB What are the cosets of the ring R=Z_4[x]/((x^2+1)*Z_4[x])?
  • · Replies 3 ·
Replies
3
Views
3K
High School Is a Matrix of Only Diagonal Ones Always Equal to its Transpose?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is a Quadratic Nonresidue of Odd Primes p and q Also a Nonresidue Modulo pq?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Solving Sum of Integers for Given Constraints
  • · Replies 2 ·
Replies
2
Views
3K
MHB Elements of a Ring: R Has 64 Elements
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Graphing Cartesian Products and Unions: Set Theory Sketches
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Proof of Sylow: Let G be a Finite Group, H and K Subgroups of G
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Implicit isomorphism involved in extension/sub fields/structures?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Nullity of a Matrix: Find the Answer
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Edge Colouring of Bipartite Graphs: Proving Valency Equality
  • · Replies 1 ·
Replies
1
Views
2K
Graduate 3D Transformation of Rectangle to a Plane
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What is the Dimension of the Subspace of M2;2 with Zero Diagonal Entries?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Is Absolute Convergence Required for Evaluating Sums over Rational Numbers?
  • · Replies 4 ·
Replies
4
Views
4K
MHB Can the Kernel of a Ring Homomorphism Equal 12Z or 13Z?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate What Are the Rules for Element and Subgroup Orders in Group Theory?
  • · Replies 3 ·
Replies
3
Views
3K
High School Understanding the Paradox of 0 Divided by 0: Is it 0 or Undefined?
  • · Replies 65 ·
3
Replies
65
Views
18K
Graduate Proving Non-Abelian Groups Have Unique Elements with Non-Commutative Properties
  • · Replies 5 ·
Replies
5
Views
3K
High School Choosing the Right Point to Start Building Your Ship
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Reflections and Reflection Groups - Basic Geometry
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Having trouble working with modules
  • · Replies 6 ·
Replies
6
Views
2K
MHB Homomorphism of Rings & Is Map f:C->Z a Homo?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Could someone explain this to me please?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Equivalence of definitions for regular representations
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Short Exact Sequences: Splitting
  • · Replies 2 ·
Replies
2
Views
3K
MHB What are the Abelian Groups of Order 1000 Containing Specific Elements?
  • · Replies 2 ·
Replies
2
Views
6K
Graduate Discover the Proof for Primes: Solving the Mystery of Interesting Sets"
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Understanding Sylow Subgroups of S4: The Logic Behind Grouping Elements
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Taking vectors from one basis to another [Byron and Fuller]
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Euclidean Reflection Groups _ Kane's text
  • · Replies 1 ·
Replies
1
Views
2K
Graduate How to Handle Zero Eigenvalues in the Generalized Eigenvalue Problem?
  • · Replies 2 ·
Replies
2
Views
4K
Undergrad Matrix of a linear transformation for an integral?
  • · Replies 3 ·
Replies
3
Views
10K
Undergrad Row Vectors vs. Column Vectors - What's the difference?
  • · Replies 5 ·
Replies
5
Views
15K
Graduate Is {S,+,.} with S = {matrix(a,b,a-b,a)|a,b ∊ R} a Field?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What are the orders of (x,v) and (x,u²) in A x B?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding Group Theory in Physics
  • · Replies 9 ·
Replies
9
Views
4K
Graduate The definition of 'reducible' in Hungerford's Algebra text
  • · Replies 2 ·
Replies
2
Views
2K
MHB Matrix Theory....showing that matrix is Unitary
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Are There Common Patterns in Group Elements and Associativity Axioms in Tables?
  • · Replies 9 ·
Replies
9
Views
2K
Graduate Infinitely many primes in every row of array
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Need for Separate Basis for Kernel: Explained by Hello
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Can Eigenvectors of the Same Eigenvalue Be Orthogonal in a 2x2 Matrix?
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Proving Schwarz inequaltiy - how to begin
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Is 3 Divisible by n if 3 is Divisible by n^2?
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Difficult theoretical problem on basis vectors
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to Solve the Extended Sylvester Equation?
  • · Replies 3 ·
Replies
3
Views
4K
Graduate Find the equivalance of AB and BC
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Find T with Subspace S as Kernel of T
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Exponent of matrix/Diagonalization of matrix with repeated eigenvalue
  • · Replies 1 ·
Replies
1
Views
3K
MHB Group homomorphism and subgroups
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Cancellation Law in Group Theory: Proof and Validity
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Does SO(3) Have Nontrivial Complex 2-Dimensional Representations?
  • · Replies 2 ·
Replies
2
Views
8K
Graduate What Does Converting a Matrix to Tridiagonal Form Indicate in Practical Terms?
  • · Replies 13 ·
Replies
13
Views
6K
Graduate Understanding Identity Elements in Abstract Binary Operations
  • · Replies 2 ·
Replies
2
Views
2K
Graduate A question about simple Weyl reflections
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Having trouble understanding a dimension reduction step in a matrix.
  • · Replies 6 ·
Replies
6
Views
3K
Graduate What Is the Condition Number of This Piecewise Function?
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Is the Generated Set of a Group Closed Under Group Operation?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Eigenvalues of a tridiagonal matrix
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Can Abstract Algebra Inspire New Tools for Ruler and Compass Constructions?
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Horner's Method vs (x-1)^n: Which is More Accurate for Evaluating Polynomials?
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad How Do You Solve a Parametric Vector Equation for a Line?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Can the Empty Set Span the Zero Subspace? Insights on Spanning Sets
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Example of PID and its maximal ideal
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Can the Graham-Schmidt Process Start with Any Vector?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Please check my solution to this invertibility test
  • · Replies 13 ·
Replies
13
Views
3K
Graduate Decompose number in Gaussian interger field
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Is A + 2A^(-1) Invertible If A Is Invertible?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Finding the Product of Primes: A Number Theory Puzzle
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Show that these vectors are in a vector space?
  • · Replies 6 ·
Replies
6
Views
7K
Undergrad Is This New Algorithm Effective for Finding Common Factors?
  • · Replies 20 ·
Replies
20
Views
5K
Undergrad Finding SVD of Matrix H: Summing H1 and H2's SVD Values?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Is a Commutative Group with a^2=1 Always a Group?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Numbers which are not ultimately functions of integers
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad A question about quadratic residues
  • · Replies 1 ·
Replies
1
Views
3K