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.
Does a Group Action Always Use the Group's Original Operation?
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Why Doesn't the Tensor Identity Work Out?
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Is the other Gram-Schmidt process truly different from the usual one?
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Are functionals and operators the same thing?
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MHB Can You Find a Counterexample for This Module Over a Commutative Ring?
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MHB Existence of a Basis of a Vector Space
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Irreducible central elements generate maximal ideals?
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Understanding Gauss-Jordan Method for Solving Equations
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MHB Verifying Answers to True/False Questions about Matrices
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MHB Finding Solutions for a System of Linear Equations with 2 Degrees of Freedom
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MHB Canonical Isomorphism and Tensor Products
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MHB Understanding Tensors: Finding the Value of a Tensor
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MHB Exterior Power of Linear Transformation
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MHB Direct Products and Quotient Groups
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MHB Prove the following; (vector spaces and linear operators)
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MHB Quotient Groups - Dummit and Foote, Section 3.1, Exercise 17
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Triangle Inequality in 'Linear Algebra Done Right'
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Cosine Similarity: Explained and Examples
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MHB Solving for $F(v,f)$ in Tensor $F$
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MHB Solution: What is Decomposable Tensor?
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Conveying inner product with words
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Systems of equations with many equations, more than 3
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Multiplication bloards after factorization
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Matrix Diagonalization & Eigen Decomposition
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Mean value(centroid) of a collection of vectors
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How Can Tensor Decomposition Be Achieved Using Linear Methods?
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Why is the Binomial Formula a Derivation?
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Ambiguity in the term 'dimension'?
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How to find the manifold associated with a Lie Group?
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MHB Orientation-preserving isometry of R^n
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MHB Transforming a Linear Transformation Matrix to an Orthonormal Basis
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MHB Arithmetic Geometry on 2-sphere: Mordell-Weil Finiteness
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Span of a Set of Linear Transformations
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MHB Finding GCD in Gaussian Integers
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MHB Uniquely Determined Linear Operator
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MHB Permutation representation argument validity
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MHB Let f(x) = x^2 + 1 and g(x) = x^3 + 1.
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Inner Product vs Dot Product: Understanding the Difference
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MHB Classify Quadratic Surfaces: Ellipsoids, Hyperboloids, Paraboloids & Cylinders
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Difference between the A conjugate and A dagger
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Determinants between two similar matrices
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Two linear transformations agree, subspace
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Cartesian Product of Permutations?
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Ring of Polynomials and Ring of Polynomial Functions
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Maximal ideal (x,y) - and then primary ideal (x,y)^n
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Analytic expression to find the range of non-negative numbers in array
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Creating a matrix with desirable eigenvalues
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MHB How to Find \(a^2\) from a Matrix Inverse Equation?
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MHB Primary Ideals, prime ideals and maximal ideals.
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MHB Finding element of inverse matrix
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MHB Maximal ideal (x,y) - and then primary ideal (x,y)^n
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MHB Normal Form and Canonical Form of a Quadratic
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MHB Orthogonal Transformation in Euclidean Space
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MHB Stabilizer subgroups - proof verification
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MHB Surjectivity for permutation representation of a group action
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MHB Is the Ideal (x) in k[x, y] a Prime Ideal?
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Why is (x) a prime ideal in k[x,y]?
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MHB Is the Projection Operator Self-Adjoint Only with Orthogonal Subspaces?
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MHB Prove Primary Ideals in \mathbb{Z}: Peter's Questions Answered
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MHB Canonical Basis and Standard Basis
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MHB How Can I Visualize a $\pi/2$ Rotation About $(1,1,0)^t$ in $\mathbb{R}^3$?
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Proving Primary Ideals in \mathbb{Z}: Peter's Challenge
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MHB Eigenvector and eigenvalue for differential operator
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Newbie question: Algebra of Mahalanobis distance
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What is the volume of these special n-dimensional ellipsoids?
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MHB Primary Ideals, prime ideals and maximal ideals - D&F Section 15.2
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Simple conceptual misunderstanding
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MHB Reducing Quadratic Form to Principle Axes
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Primary Ideals, prime ideals and maximal ideals - D&F Section 15.2
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Isomorphic Finite Dimensional Vector Spaces
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Simple question about parametric equations of a plane in 3D
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Affine Varieties - the x-axis in R^2
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Primary Ideals, prime ideals and maximal ideals.
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Is SO(2) Considered a Lie Group?
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MHB How Do You Invert This 2x2 Matrix?
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Proving Convexity of a Set: A Proof by Contradiction Approach
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Affine Varieties - Single Points and maximal ideals
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MHB Questions about Jordan Normal Form
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MHB Mapping and inverse mapping of open sets and their complements
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MHB Indexes of inertia for the function
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Spinor representations decomposed under subgroups in Joe's big book
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MHB Prove G is a Subspace of V ⊕ V and Quotient Space (V ⊕ V)/G Isomorphic to V
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MHB Hermitian Function Proof: Correcting a Mistake
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MHB Dimension of the space of skew-symmetric bilinear functions
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MHB Is the Function f Non-Singular and Positive?
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Different Versions of a Plane in R^3 (The Plane, The Plane)
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What Can Be Said About the Rows and Columns of \(A^TA\)?
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MHB Orders of elements for rotational symmetries of cube
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Algebriac Geometry - Morphisms of Algebraic Sets
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Algebriac Geometry - Morphisms of Algebraic Sets
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MHB Prove $R\ncong R\left[x\right]$ for Noetherian Ring
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MHB Prove that the quotient space R^n / U is isomorphic to the subspace W
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Row/Column space in relation to row operations
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Affine transformations and their inverse
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Can Linear Transformations Occur Between Infinite and Finite Dimensions?
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How to find the number of elements with a particular order in a group?
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Composition of Functions - in the context of morphisms in algebraic ge
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MHB Condition Number of sum of Matrices
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How Do Eigenvalues and Eigenvectors Connect to Fourier Transforms?
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Direction of a vector relative to another vector?
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