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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.
MHB How Does the Correspondence Theorem for Rings Prove Maximal Ideals?
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Undergrad Maximal Ideals and the Correspondence Theorem for Rings
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MHB Normal Extensions and Normal Subgroups
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MHB A little problem on exact sequences.
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Undergrad Transpose Property (where's my mistake)
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Undergrad A double in this example problem
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Undergrad Show that the diagonals are perpendicular using vectors
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Undergrad Use Lorentz Force to Find Magnetic Field Components
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Undergrad Matrix Component Equation: Solving for B with Known Scalar and Indices
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Undergrad Kronecker Delta summation (easy)
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MHB Prove: \(F(a,b)^*=F(a) \cup F(b)\)
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Undergrad Two-sided Prinicipal Ideal - the Noncommutative Case - D&F
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MHB Why Is the Set {ras | r, s ∈ R} Not a Two-Sided Ideal in Noncommutative Rings?
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Undergrad Understanding SU(2) Representations and Their Role in Particle Physics
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Undergrad Module Over a Division Ring - Blyth Theorem 1.1, Part 4
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Undergrad State of a Generator in Representation Theory
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High School Tensor Calculus vs Tensor Analysis?
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Undergrad What is the name of the matrix decomposition with specific properties?
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Undergrad No problem, it's always good to have multiple sources!
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MHB Finding the zero vector of a sinusoidal set
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MHB Submodules A + B and A intersect B .... Blyth Ch. 2
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Undergrad Submodules A + B and A intersect B .... Blyth Ch. 2
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MHB Theorem 2.3: Submodule Generation by Family of Submodules - T. S. Blyth
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Undergrad Submodule Generated by Family of Submodules -Simple Question
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Undergrad Interpretation of direct product of Hilbert spaces
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Undergrad Coordinate System: Understanding Polar Vectors
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Graduate What Is the Spectrum of a Linear Operator in L2 Spaces?
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MHB Making a Right R-module Into a Left R-Module - Bland, page 26 ....
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Undergrad Split Exact Sequences .... Bland, Proposition 3.2.7
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MHB Module Over a Division Ring - Blyth Theorem 1.1, Part 4
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MHB How Does Condition (2) Imply Condition (3) in Bland's Proposition 3.2.7?
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Undergrad Eigenvalue as a generalization of frequency
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Undergrad Proving Vector Space of Circles is Not Axiomatic
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High School Polynomial Space: Can Degree 2 Fit in 1+x^2?
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MHB Finitely Cogenerated Modules - Bland Definition 4.1.3, Page 105
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Undergrad Question in linear algebra, derivation of a certain relation
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MHB Bland - Rings and their Modules 2011
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High School Understanding Choi's Theorem and Notation in Matrix Theory
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MHB Each exact sequence can be arised by short exact sequences
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MHB Exact Sequences and short exact sequences - basic question
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Graduate Hodge Dual as Sequence of Grade Reducing Steps
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Undergrad Simplifying 3 simultaneous equation into one equation
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Graduate Rank 3x4 Complex Matrix Constraints
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Graduate Normalization and Scaling with Matrices
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Undergrad Solving equations with singular matrix
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Undergrad Vector components, scalars & coordinate independence
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Undergrad Unraveling Representations of SU2 & SU3 in Particle Physics
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Undergrad Tensor product and ultraproduct construction
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MHB Help with Projective Algebraic Geometry - Cox et al Section 8.1, Exs 5(a) & 5(b)
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Undergrad Create an Equation for 3 Offspring Rabbits
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MHB Show that $p(x)|f(x)$: Proving the Divisibility
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High School Mistake when explaining associativity of vector addition
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MHB Projective Algebraic Geometry - Exercise 4(a) Cox et al - Section 8.1
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Graduate How Did They Derive Equation (49) from Equation (21) Using Matrix Identities?
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Undergrad Parametric Representation of a Solution Set
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MHB Projective Algebraic Geometry - the Projective Plane ....
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MHB Help with Exercise 3(c) in Cox et al's Projective Algebraic Geometry
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Undergrad Make a Perfect Dodecahedron: What Angle to Cut Plywood?
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MHB Peter Needs Help on Cox et al - Section 8.1, Exercise 3(a)
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Undergrad Is Geometric Algebra inconsistent/circular?
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Undergrad Question about decomposition of matrices in SL(2,R)
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Graduate Exterior Algebra Dual for Cross Product & Rank 2 Tensor Det
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MHB Finding a set of vectors that span u,v....
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MHB Algebraic element - Minimal polynomial
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MHB Prime Subfield of Field F: Isomorphic to $\mathbb{Q}$
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High School Sets and functions that gain more structure with context
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MHB How to find a non-zero vector in the column space of M
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MHB How can I find out if this matrix A's columns are linearly independent?
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Undergrad Dimension of the group O(n,R) - How to calc?
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Undergrad Vector Division: An Explainer of Why It's Not Possible
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What Are Imaginary Numbers and How Can They Be Understood?
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Undergrad Why is this Isometry a rotation?
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MHB Find all the matrices in Jordan form
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MHB Wondering if $R$ is a P.I.D.: Free Modules and Ideals
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MHB Ideals and GCDs in k[x] .... .... Cox Et al: "Ideals, Varieties and Algorithms"
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MHB Is \(F[x]/<p(x)>\) the Root Field of \(x^4+ax^2+b\)?
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Undergrad Algebraically Closed Fields
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MHB How Does Algebraic Closure Extend to Multivariable Polynomials?
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MHB Ideals in Q[x, y] .... Cox, Little and O'Shea, Chapter 1 Section 4
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MHB Affine Algebraic Sets in A^2 - Dummit and Foote, page 660, Example 3
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Undergrad Eigenvalues and Eigenvectors question
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MHB Show Im(gf)=Im(g) When f is Onto (Wondering)
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Undergrad Affine Algebraic Sets - General Question
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Graduate What is the state of the art in solving polynomial equations?
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Undergrad Proving Isometries: A Step-By-Step Guide
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Graduate Why Is the Discriminant Non-Positive in the Triangle Inequality Proof?
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Graduate Understanding the Eigenframe: Definition and Importance
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Undergrad SU(2) and su(2) have different dimensions?
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Undergrad Affine Algebraic Sets - Dummit and Foote, page 660, Ex. 3
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Undergrad What is the Inverse of the Function f(x) = e^x + e^(-x) + 1?
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Undergrad Why do some people only define prime elements in integral domains?
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Undergrad Proving Identity for Determinant of $A^tA$
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MHB Equivalence of Definitions of Algebras in D&F and Cooperstein | Peter
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Undergrad K-algebra/associative algebra - equivalence of definitions
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Undergrad Polynomials in n indeterminates and UFDs
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MHB Prime Elements in Non-Integral Domains?
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MHB Statements about subrings and quotient
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MHB Polynomials in n indeterminates and UFDs
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Undergrad Difference between direct sum and direct product
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Undergrad Chladni plate with Neumann conditions
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