Linear and Abstract Algebra Forum

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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 What Maps Belong to Aut(S2)/SO(3)?
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Graduate How to prove the field extension is algebraically closed
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Graduate Adding a constant times the unit matrix and eigenvalues
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Undergrad Good method for checking solutions to linear systems of equations by hand
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Graduate Coefficients of the characteristic equation
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Graduate How to solve a system of linear inequalities with absolute magnitudes?
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Undergrad AP vs. CPAP: Which is Best for Sleep Apnea?
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Graduate Is (2X,5) Really an Ideal in Z[X]?
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Graduate Difference between product and pullback
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Undergrad Discover the Pattern of PDS Numbers and Find the Nth PDS Number
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MHB System of Equations: (2x-1)(2y-1)
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High School What is a nonconstant linear function?
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Graduate Is Every Norm on a Finite-Dimensional Vector Space Induced by an Inner Product?
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Graduate How to find subgroup of index n in a given group
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Undergrad Solbing equation A(u)=B(v) for square matrices A and B
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Graduate Ring Homomorphism - showing Multiplicativity
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Graduate Proof about a prime between k and 2k.
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Undergrad Can Solving n = x (mod 10x+1) Simplify Factoring Numbers?
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Graduate Is the Set {cos x, cos 2x, cos 3x, ...} Orthogonal Using Integral Products?
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Graduate What is the latest on the Group Extension Problem?
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MHB Linear independence of polynomial set.
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Graduate Efficient Anti-Triangular Matrix Multiplications
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Undergrad How Does the Variable x Relate to n in This Divisibility Problem?
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Graduate Is Physical Symmetry Limited Due To The Classification Theorem?
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Graduate Optimizing Bi-Linear Objective Function for Vector Fitting in Flat Space
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Undergrad Question about Multiplying Matrices
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Graduate Is 2Z isomorphic to 4Z? (Abstract algebra)
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MHB What are the cosets of the ring R=Z_4[x]/((x^2+1)*Z_4[x])?
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High School Is a Matrix of Only Diagonal Ones Always Equal to its Transpose?
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Graduate Is a Quadratic Nonresidue of Odd Primes p and q Also a Nonresidue Modulo pq?
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Undergrad Solving Sum of Integers for Given Constraints
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MHB Elements of a Ring: R Has 64 Elements
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Undergrad Graphing Cartesian Products and Unions: Set Theory Sketches
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Graduate Proof of Sylow: Let G be a Finite Group, H and K Subgroups of G
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Graduate Implicit isomorphism involved in extension/sub fields/structures?
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Undergrad Nullity of a Matrix: Find the Answer
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Graduate Edge Colouring of Bipartite Graphs: Proving Valency Equality
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Graduate 3D Transformation of Rectangle to a Plane
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Undergrad What is the Dimension of the Subspace of M2;2 with Zero Diagonal Entries?
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Graduate Is Absolute Convergence Required for Evaluating Sums over Rational Numbers?
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MHB Can the Kernel of a Ring Homomorphism Equal 12Z or 13Z?
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Graduate What Are the Rules for Element and Subgroup Orders in Group Theory?
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High School Understanding the Paradox of 0 Divided by 0: Is it 0 or Undefined?
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Graduate Proving Non-Abelian Groups Have Unique Elements with Non-Commutative Properties
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High School Choosing the Right Point to Start Building Your Ship
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Graduate Reflections and Reflection Groups - Basic Geometry
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Graduate Having trouble working with modules
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MHB Homomorphism of Rings & Is Map f:C->Z a Homo?
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Graduate Could someone explain this to me please?
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Graduate Equivalence of definitions for regular representations
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Graduate Short Exact Sequences: Splitting
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MHB What are the Abelian Groups of Order 1000 Containing Specific Elements?
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Graduate Discover the Proof for Primes: Solving the Mystery of Interesting Sets"
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Graduate Understanding Sylow Subgroups of S4: The Logic Behind Grouping Elements
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Graduate Taking vectors from one basis to another [Byron and Fuller]
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Graduate Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture
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Graduate Euclidean Reflection Groups _ Kane's text
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Graduate How to Handle Zero Eigenvalues in the Generalized Eigenvalue Problem?
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Undergrad Matrix of a linear transformation for an integral?
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Undergrad Row Vectors vs. Column Vectors - What's the difference?
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Graduate Is {S,+,.} with S = {matrix(a,b,a-b,a)|a,b ∊ R} a Field?
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Graduate What are the orders of (x,v) and (x,u²) in A x B?
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Graduate Understanding Group Theory in Physics
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Graduate The definition of 'reducible' in Hungerford's Algebra text
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MHB Matrix Theory....showing that matrix is Unitary
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Graduate Are There Common Patterns in Group Elements and Associativity Axioms in Tables?
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Graduate Infinitely many primes in every row of array
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Undergrad Need for Separate Basis for Kernel: Explained by Hello
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Undergrad Can Eigenvectors of the Same Eigenvalue Be Orthogonal in a 2x2 Matrix?
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Graduate Proving Schwarz inequaltiy - how to begin
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Undergrad Is 3 Divisible by n if 3 is Divisible by n^2?
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Graduate Difficult theoretical problem on basis vectors
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Graduate How to Solve the Extended Sylvester Equation?
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Graduate Find the equivalance of AB and BC
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Graduate Find T with Subspace S as Kernel of T
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Graduate Exponent of matrix/Diagonalization of matrix with repeated eigenvalue
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MHB Group homomorphism and subgroups
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Graduate Cancellation Law in Group Theory: Proof and Validity
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Graduate Does SO(3) Have Nontrivial Complex 2-Dimensional Representations?
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Graduate What Does Converting a Matrix to Tridiagonal Form Indicate in Practical Terms?
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Graduate Understanding Identity Elements in Abstract Binary Operations
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Graduate A question about simple Weyl reflections
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Graduate Having trouble understanding a dimension reduction step in a matrix.
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Graduate What Is the Condition Number of This Piecewise Function?
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Graduate Is the Generated Set of a Group Closed Under Group Operation?
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Graduate Eigenvalues of a tridiagonal matrix
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Graduate Can Abstract Algebra Inspire New Tools for Ruler and Compass Constructions?
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Undergrad Horner's Method vs (x-1)^n: Which is More Accurate for Evaluating Polynomials?
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Undergrad How Do You Solve a Parametric Vector Equation for a Line?
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Undergrad Can the Empty Set Span the Zero Subspace? Insights on Spanning Sets
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Graduate Example of PID and its maximal ideal
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Undergrad Can the Graham-Schmidt Process Start with Any Vector?
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Graduate Please check my solution to this invertibility test
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Graduate Decompose number in Gaussian interger field
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Graduate Is A + 2A^(-1) Invertible If A Is Invertible?
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Undergrad Finding the Product of Primes: A Number Theory Puzzle
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Undergrad Show that these vectors are in a vector space?
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Undergrad Is This New Algorithm Effective for Finding Common Factors?
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Undergrad Finding SVD of Matrix H: Summing H1 and H2's SVD Values?
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Graduate Is a Commutative Group with a^2=1 Always a Group?
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