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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.
Undergrad Correspondence Theorem for Groups .... Rotman, Propn 1.82 ....
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MHB The Correspondence Theorem for Groups .... Rotman, Proposition 1.82 ....
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MHB Understanding Null Space and Column Space of a Matrix
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MHB What Causes Discrepancies Between Rational Root Test and Modulo p Methods?
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MHB Third Isomorphism Theorem for Rings .... Bland Theorem 3.3.16 .... ....
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Undergrad Third Isomorphism Theorem for Rings .... Bland Theorem 3.3.16
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Undergrad Second Isomorphism Theorem for Rings .... Bland Theorem 3.3.1
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MHB Polynomial Proof: Verification & Correction
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MHB Second Isomorphism Theorem for Rings .... Bland Theorem 3.3.15 .... ....
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Undergrad Quotient Rings .... Remarks by Adkins and Weintraub ....
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MHB Find determinant by row reduction in echelon
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MHB Quotient Rings .... Remarks by Adkins and Weintraub ....
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MHB Is x^4+x^3+1 Irreducible in Q[x] and Z[x]?
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MHB Solve Part (b) of Nonzero Polynomials | Help Needed
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Undergrad Representation Theory clarification
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Undergrad Finite Integral Domains .... Adkins & Weintraub, Propn 1.5
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Undergrad Understanding 4-Vector Representations in the Lorentz Group
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Undergrad Division Rings & Ring Homomorphisms .... A&W Corollary 2.4 ...
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MHB Problem about equivalent conditions for a basis of a free module
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MHB Finite Integral Domains .... Adkins & Weintraub, Proposition 1.5 ....
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Undergrad What is the definition of a Semi-simple Lie algebra?
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MHB Solving Inequalities Involving |x+2| & |x2 -3ax+2a2|
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MHB Question about proof of the linear independence of a dual basis
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Undergrad Solutions to equations involving linear transformations
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MHB Simple Modules and Maximal Right Ideals .... Bland, Proposition 6.1.7 ....
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Undergrad Understanding Hilbert Vector Spaces
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MHB A problem about submodules in "Advanced Modern Algebra" of Rotman
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MHB Proving Finite subgroups of the multiplicative group of a field are cyclic
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Undergrad Can we construct a Lie algebra from the squares of SU(1,1)
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Graduate What separates Hilbert space from other spaces?
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Undergrad 1st year linear algebra question
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Graduate Understanding the Difference: Spectra of Unbounded vs. Bounded Operators
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Undergrad Proving that an operator is unbounded
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MHB Verifying Answers to "Zero Divisors & Isomorphism Theorem"
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Undergrad Geometric intuition of a rank formula
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Graduate Understanding Complex Operators: Rules, Boundedness, and Positivity
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Undergrad Understanding the Vector Triple Product Proof
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Undergrad How to Synthesize Orthogonal Transformation Matrix T?
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MHB Layout Notation for matrix calculus
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Undergrad Splitting ring of polynomials - why is this result unfindable?
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Graduate Why a Lie Group is closed in GL(n,C)?
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Graduate Example of how a rotation matrix preserves symmetry of PDE
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Undergrad Question about inverse operators differential operators
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MHB Is My Solution to Part B of the Math Question Correct?
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MHB Verifying Solutions to Isomorphism Problem: Need Help!
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Graduate Does Commutativity Affect Linearity?
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Undergrad Is a commutative A-algebra algebraic over A associative?
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MHB Help with Part (a) & (b) of Question - Appreciate Assistance!
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Undergrad Is there a geometric interpretation of orthogonal functions?
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Undergrad What are the differences between matrices and tensors?
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Graduate Proving the Last Gauss Lemma for Real Numbers Using Induction
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Graduate Is the proof of these results correct?
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Undergrad How to find admissible functions for a domain?
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MHB Congruence Class Proofs: Tips and Examples
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Graduate Reality conditions on representations of classical groups
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MHB How many homomorphisms are there from $\mathbb{Z}_4$ to $S_4$?
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MHB [Linear Algebra] - Find the shortest distance d between two lines
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Graduate Hilbert-adjoint operator vs self-adjoint operator
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Undergrad Projective Representations: a simple example
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Undergrad Non-Hermitian wavefunctions and their solutions
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MHB Show that the determinant is equal to 0
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MHB Troubleshooting Euclid's Lemma Proof in Modular Arithmetic
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How Does Least Squares Determine the Mean and Variance?
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Undergrad Diagonalization and change of basis
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Undergrad Is there a ket to correspond to every bra?
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MHB The Determinant of a Matrix with n+1 Ones: Is It Always -1, 0, or 1?
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MHB Solving Linear Equations: $Ax=b$ and Rank of A
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Graduate The meaning of the commutator for two operators
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Graduate Eigenvalue Problem and the Calculus of Variations
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Graduate Second derivative of a complex matrix
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MHB Determining Value of a in Matrix A with $\lambda$ = 0
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MHB Showing that a matrix is a homomorphism
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MHB Is B Equal to A³ Given Symmetric and Invertible Matrices?
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MHB What is the basis of the trivial vector space {0}
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High School How Can You Determine if an Operator is Surjective, Injective, or Bijective?
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Undergrad What are the groups for NxNxN puzzle cubes called?
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Graduate Are bounded operators bounded indepedently on the function?
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Undergrad Need clarification on a theorem about field extensions/isomorphisms
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Undergrad Do Two Eigenvectors Form a Hilbert Space with Their Inner Product?
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High School Can Linear Combinations in Quantum Mechanics Include Multiplication of States?
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MHB Singular Values and Eigenvalues
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MHB Proving Matrix Equality Using Singular Value Decomposition
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Graduate Is this operator bounded or unbounded?
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MHB Orthonormal Basis times a real Matrix
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Undergrad "Banana clock shapes" puzzle on social media
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Graduate Operator mapping in Hilbert space
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Undergrad Measures of Linear Independence?
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MHB How to Compute Coordinate Column Vectors in Different Bases?
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Graduate How many cosets are there when taking a subgroup in a group and forming cosets?
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High School Why do equations with two distinct variables with 2 distinct
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Inverse linear algebra problem for stereo triangulation
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High School Tensor Product, Basis Vectors and Tensor Components
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High School Linearizing a Relation: How to Create a Best Fit Linear Line in Logger Pro
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MHB Intersection of all subspace of V is the empty set
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Undergrad Relationship between a non-Hermitian Hamiltonian and its solution
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MHB Describe bases for the span of sets
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Finding Angles of Triangle Given Two Points on Earth and One in Space
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Undergrad Consequences on a system of ODEs after performing operations
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Undergrad Types of complex matrices, why only 3?
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Undergrad A different way to express the span
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