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.
Matrix Multiplication and Commuting
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Describing Matrix/Transformation by Eigens.
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How to calculate complex dot products
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Relationship between eigenspace and column space
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Confusion between orthogonal sum and orthogonal direct sum
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Relationship between column space of a matrix and rref of matrix
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Lanczos Method: Calculating Smallest Eigenvalues
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Can a nonabelian group of order p^3 be constructed for any prime p?
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Mathematica Vector Fields Explaination.
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Various Proofs Regarding Divisors and Properties of Divisors
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Definition questions for linear algebra
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Linear Algebra Proof of Span and orthogonal vector space
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3K
MHB Are Units and Principal Ideals Related in Rings?
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Maximal number of bases for which composite number is Fermat pseudoprime
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Solving Vector Norm with F Matrix: Advice from Jo
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Meaning of eigenvectors and values of a 2x2 matrix (2nd order tensor)
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How Can the Fibonacci Sequence Be Proved by Induction?
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Can Eigenvalues of Matrix Addition Be Simplified?
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What Does \Re2 \rightarrow \Re2 Mean in Linear Transformations?
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Is f(a) Always 1 or Legendre Symbol?
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10
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MHB Solving for Unit Vectors in U Given Vector 1 and Matrix S
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How to prove that pZ is a maximal ideal for the ring of integers?
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Picard-Vessiot Extension over a Differential Field?
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3
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MHB Proving Orthogonal Polynomials: A Weighted Integral
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Where does p = 5 (mod 8) solve x^2 = a?
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A≡b mod n true in ring of algebraic integers => true in ring of integers
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Is the Degree of Q(a) Over Q Correctly Understood?
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How do you solve equations with matrices?
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Diagonalization and similar matrices
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What Maps Belong to Aut(S2)/SO(3)?
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15
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How to prove the field extension is algebraically closed
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Adding a constant times the unit matrix and eigenvalues
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Good method for checking solutions to linear systems of equations by hand
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Coefficients of the characteristic equation
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How to solve a system of linear inequalities with absolute magnitudes?
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AP vs. CPAP: Which is Best for Sleep Apnea?
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Is (2X,5) Really an Ideal in Z[X]?
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Difference between product and pullback
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Discover the Pattern of PDS Numbers and Find the Nth PDS Number
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What is a nonconstant linear function?
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Is Every Norm on a Finite-Dimensional Vector Space Induced by an Inner Product?
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How to find subgroup of index n in a given group
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Solbing equation A(u)=B(v) for square matrices A and B
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Proof about a prime between k and 2k.
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Can Solving n = x (mod 10x+1) Simplify Factoring Numbers?
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Is the Set {cos x, cos 2x, cos 3x, ...} Orthogonal Using Integral Products?
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What is the latest on the Group Extension Problem?
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MHB Linear independence of polynomial set.
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Efficient Anti-Triangular Matrix Multiplications
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How Does the Variable x Relate to n in This Divisibility Problem?
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Is Physical Symmetry Limited Due To The Classification Theorem?
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Question about Multiplying Matrices
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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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Is a Quadratic Nonresidue of Odd Primes p and q Also a Nonresidue Modulo pq?
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Solving Sum of Integers for Given Constraints
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MHB Elements of a Ring: R Has 64 Elements
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Graphing Cartesian Products and Unions: Set Theory Sketches
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Proof of Sylow: Let G be a Finite Group, H and K Subgroups of G
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Implicit isomorphism involved in extension/sub fields/structures?
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Nullity of a Matrix: Find the Answer
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3D Transformation of Rectangle to a Plane
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What is the Dimension of the Subspace of M2;2 with Zero Diagonal Entries?
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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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What Are the Rules for Element and Subgroup Orders in Group Theory?
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Understanding the Paradox of 0 Divided by 0: Is it 0 or Undefined?
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Proving Non-Abelian Groups Have Unique Elements with Non-Commutative Properties
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Choosing the Right Point to Start Building Your Ship
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Reflections and Reflection Groups - Basic Geometry
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Having trouble working with modules
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MHB Homomorphism of Rings & Is Map f:C->Z a Homo?
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Could someone explain this to me please?
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Equivalence of definitions for regular representations
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Short Exact Sequences: Splitting
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MHB What are the Abelian Groups of Order 1000 Containing Specific Elements?
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Discover the Proof for Primes: Solving the Mystery of Interesting Sets"
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Understanding Sylow Subgroups of S4: The Logic Behind Grouping Elements
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Taking vectors from one basis to another [Byron and Fuller]
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Area of a Triangle and Elliptic Curves - Birch and Swinnerton Dyer Conjecture
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Euclidean Reflection Groups _ Kane's text
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How to Handle Zero Eigenvalues in the Generalized Eigenvalue Problem?
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Matrix of a linear transformation for an integral?
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Is {S,+,.} with S = {matrix(a,b,a-b,a)|a,b ∊ R} a Field?
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What are the orders of (x,v) and (x,u²) in A x B?
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Understanding Group Theory in Physics
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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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Are There Common Patterns in Group Elements and Associativity Axioms in Tables?
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Infinitely many primes in every row of array
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Need for Separate Basis for Kernel: Explained by Hello
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Can Eigenvectors of the Same Eigenvalue Be Orthogonal in a 2x2 Matrix?
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Proving Schwarz inequaltiy - how to begin
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Is 3 Divisible by n if 3 is Divisible by n^2?
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Difficult theoretical problem on basis vectors
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How to Solve the Extended Sylvester Equation?
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Find the equivalance of AB and BC
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Find T with Subspace S as Kernel of T
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Exponent of matrix/Diagonalization of matrix with repeated eigenvalue
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MHB Group homomorphism and subgroups
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