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.
Understanding the abstract notion of an vector space
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Is Levy-Desplanques Theorem limited to specific values of i and M?
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What is a vector valued in a function?
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How to Calculate π^σ If We Have 2 Disjoint Cycles?
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How to calculate center coordinates of two reverse arcs in 3D space
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How to find unique solution of X
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Misunderstanding a Theorem on Field Homomorphism
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Factoring Algorithms for Exponential Speed | Tips & Advice
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Why are certain transformations in the case of D4 group considered even or odd?
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Factor (Quotient) Space definitions.
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Solutions of a system of linear equations
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Quick definition question: Dihedral group
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Can the inverse of a matrix exponential be proven using its definition?
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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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An extension of Dot and Cross Product
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MHB The Ideal (x1, x2, .... .... xn)^m
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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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Stuck on Rank(G/H) = Rank(G) - Rank(H) Should be trivial(?)
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What Symmetry Group Does the Quantum Harmonic Oscillator Exhibit?
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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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Face of face of a cone is a face. Proof?
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Levi-Civita Tensor & Group Theory: Symmetry?
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Group Theory, unitary representation and positive eigenvalues
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Injective endomorphism = Surjective endomorphism
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Ray tracing, regarding Turner Whitted's original paper
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MHB Polynomial Rings - Lemma 1.13 from Sharp: Steps in Commutative Algebra
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Kernels and determinants of a matrix
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What is the minimum rank of a skew symmetric matrix?
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Is Dimension 3 Enough to Prove Isomorphism Between Spaces?
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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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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 Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.
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What is the New Definition of Conformal Transformations?
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Number of jordan blocks in Jordan decomposition
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Basic Question: Order of permutations in Sn
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How to visualise bilinear form and inner products?
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Short Exact Sequences 0→A→B→C→0: Explained
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Cosets: difference between these two statements
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Do Orthogonal Subsets Spanning the Same Subspace Prove Equality?
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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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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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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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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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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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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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Multiple Choise Questions in Calculus/Algebra/Electromagnetism
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MHB Number of elements and subgroups
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Understanding Low Rank Approximation with SVD: A Comprehensive Guide
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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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Are orthonormal eigenbases unique?
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MHB What is the fastest method for computing determinants?
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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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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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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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Product of two Minkowksi metrics
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MHB Distance Between a Subspace and a Vector
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Determinant of a unit columns matrix
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Call for help in finding approximate inverse matrix
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MHB Distance from a vector to a subspace
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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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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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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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Abstract algebra: elements of fiber writable as
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Difference between line vector and free vector
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Is R/kZ under multiplication a field?
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Understanding the Normal Operator Equality in Proofs of Properties
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MHB How Do You Convert Expressions into Bilinear Form?
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MHB Dummit and Foote - Definition of Zn - Motivation?
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