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.
Undergrad What is a vector valued in a function?
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Graduate How to Calculate π^σ If We Have 2 Disjoint Cycles?
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Graduate How to calculate center coordinates of two reverse arcs in 3D space
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MHB At Least p+1 p-Subgroups in Finite Group G
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Undergrad How to find unique solution of X
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Graduate Misunderstanding a Theorem on Field Homomorphism
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Graduate Factoring Algorithms for Exponential Speed | Tips & Advice
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Graduate Why are certain transformations in the case of D4 group considered even or odd?
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Undergrad Linear system in polar coordinates
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Graduate Factor (Quotient) Space definitions.
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Graduate Solutions of a system of linear equations
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Undergrad Quick definition question: Dihedral group
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Undergrad Can the inverse of a matrix exponential be proven using its definition?
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Graduate Why Is a Group with Identical Elements Considered Unfaithful?
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MHB Sums of Ideals - R. Y. Sharp "Steps in Commutative Algebra"
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MHB Union of Monoids: Is $(G\cup H,\cdot)$ A Monoid?
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Graduate An extension of Dot and Cross Product
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MHB The Ideal (x1, x2, .... .... xn)^m
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Graduate What Are the Utilities of Interior and Exterior Products?
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MHB Structure of R[X] and an exercise on ring adjunction
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Graduate Stuck on Rank(G/H) = Rank(G) - Rank(H) Should be trivial(?)
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Graduate What Symmetry Group Does the Quantum Harmonic Oscillator Exhibit?
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Undergrad Eigenvalues of 2 matrices are equal
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MHB Show Self-Adjointness of Operator E on $L_{2}$ of Square Integrable Functions
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MHB Products of ideals of K[x1, x2, x3, x4]
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MHB Residue Class Rings (Factor Rings) of Polynomials _ R Y Sharp
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MHB How Do You Solve Exercises Involving 2D and 3D Vectors and Dot Product?
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Graduate Face of face of a cone is a face. Proof?
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Graduate Levi-Civita Tensor & Group Theory: Symmetry?
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Graduate Group Theory, unitary representation and positive eigenvalues
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Graduate Injective endomorphism = Surjective endomorphism
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Undergrad Ray tracing, regarding Turner Whitted's original paper
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Undergrad Algebra with Complex Numbers & Imaginary Unit
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MHB Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
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Undergrad Kernels and determinants of a matrix
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Undergrad What is the minimum rank of a skew symmetric matrix?
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Graduate Is Dimension 3 Enough to Prove Isomorphism Between Spaces?
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Graduate Diagonalizable endomorphism has trivial null space
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MHB Using matrix to complete the square
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MHB Quasi-local commutative ring with maximal ideal M
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Graduate F=ℝ: Normal matrix with real eigenvalues but not diagonalizable
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MHB Maximal Ideals of K[X] in Commutative Algebra: A Helpful Guide
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MHB Solve 3D Vector Equation: x-int=3, z-int=-1; (x,y,z)=(p1,p2,p3)+t(d1,d2,d3)
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MHB Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.
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Graduate What is the New Definition of Conformal Transformations?
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Graduate Number of jordan blocks in Jordan decomposition
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Undergrad Basic Question: Order of permutations in Sn
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Undergrad How to visualise bilinear form and inner products?
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Graduate Short Exact Sequences 0→A→B→C→0: Explained
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Graduate Cosets: difference between these two statements
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Graduate Do Orthogonal Subsets Spanning the Same Subspace Prove Equality?
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Graduate SVD Low-Rank Approximation Algorithm
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MHB Prime Ideals in K[X] - Commutative Algebra Exercise 3.22 (ii)
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Graduate Projective Plane: Understanding "Set of Equivalence Classes" & Deleting Origin
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MHB Proving End($K^2$)=K for A-Module $K^2$
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Graduate How Can I Publish My Beal Conjecture Findings?
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MHB Linear Dependency: Max Size of Subset of Vectors
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Graduate Is it possible to express all mathematics through atomic pieces of computation?
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MHB Compute Ideal Generated by Matrix 3x3
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MHB Is \( A \) Isomorphic to \( \dfrac{R<X,Y>}{((X^2+1)X,(X^2+1)Y,YX)} \)?
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Graduate Is this homomorphism, actually isomorphism of groups?
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MHB Algebra: Generating C as an R Algebra Subject to i^2=-1
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MHB Why is Sharp's Lemma 1.10 crucial for understanding R-algebras?
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Undergrad Linear algebra, when does the implications hold?
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MHB Maximal Ideals K[X]: Solving Exercise 3.6 w/ R.Y. Sharpe
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Undergrad Multiple Choise Questions in Calculus/Algebra/Electromagnetism
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MHB Number of elements and subgroups
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Graduate Understanding Low Rank Approximation with SVD: A Comprehensive Guide
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Undergrad Are Matrix Multiplication Rules the Same for Composing Linear Transformations?
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MHB Matrix transform- about origin, then angular rotation
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Graduate Are orthonormal eigenbases unique?
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MHB What is the fastest method for computing determinants?
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Graduate Set of invertible matrices with real entries
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MHB Prove These 3 Statements About A Matrix: Rank of Adjoint
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Graduate Is $\mathcal{R}$ Lie Group Without 0?
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MHB Is the Orthogonal Complement of an Invariant Subspace Itself Invariant?
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Undergrad Orthogonal Projections vs Non-orthogonal projections?
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MHB Prove that every nonzero vector in V is a maximal vector for T.
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Graduate Product of two Minkowksi metrics
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MHB Distance Between a Subspace and a Vector
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Undergrad Determinant of a unit columns matrix
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Graduate Call for help in finding approximate inverse matrix
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MHB Distance from a vector to a subspace
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High School Comparing Vectors: Orientation vs. Direction
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MHB Elementary Algebraic Geometry - D&F Section 15.1 - Exercise 15
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MHB What is the annihilator of a tensor in vector space V?
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MHB Jordan Normal Form of Unitary Transformation
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MHB The Existence of Symmetric Matrices in Subspaces
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MHB Finding Basis of the Quotient Space
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MHB Semigroup Structure: Exploiting Non-Finitely Generated Monoids
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MHB Solving Systems of Linear Equations with ljx.m
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Undergrad Is the Matrix R Necessarily Lower Triangular in Matrix Decomposition?
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MHB Sizes of kernels of homomorphisms
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MHB Algebraic Geometry - D&F Section 15.1, Exercise 24
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MHB Parametrization of a Reduced Matrix
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Graduate Open Conditions for Matrix Groups: Understanding the Role of det(A)≠0
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MHB Partial Derivatives of Matrix/Vector Function: An Easier Way?
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Graduate Abstract algebra: elements of fiber writable as
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Graduate Difference between line vector and free vector
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Graduate Is R/kZ under multiplication a field?
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