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.
Graduate 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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Graduate Lectures on Rings: Galois Theory
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Graduate Does a Group Action Always Use the Group's Original Operation?
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Graduate Why Doesn't the Tensor Identity Work Out?
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Graduate Is the other Gram-Schmidt process truly different from the usual one?
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Graduate 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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Undergrad What is the difference between a field a subfield
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Graduate Irreducible central elements generate maximal ideals?
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MHB Help with system of equations: using profits
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Undergrad 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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Graduate Triangle Inequality in 'Linear Algebra Done Right'
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Undergrad 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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Graduate Conveying inner product with words
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Undergrad Complex Numbers as Vectors: An Exploration of Their Properties and Applications
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Undergrad Systems of equations with many equations, more than 3
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Graduate Multiplication bloards after factorization
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Undergrad Matrix Diagonalization & Eigen Decomposition
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Undergrad Mean value(centroid) of a collection of vectors
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Graduate How Can Tensor Decomposition Be Achieved Using Linear Methods?
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Graduate Why is the Binomial Formula a Derivation?
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Graduate Ambiguity in the term 'dimension'?
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Graduate 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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Undergrad 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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Undergrad Inner Product vs Dot Product: Understanding the Difference
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MHB Classify Quadratic Surfaces: Ellipsoids, Hyperboloids, Paraboloids & Cylinders
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Graduate Difference between the A conjugate and A dagger
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Undergrad Determinants between two similar matrices
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Graduate Two linear transformations agree, subspace
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Graduate Cartesian Product of Permutations?
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Undergrad Explain why matrix multiplication is not commutative.
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Graduate Ring of Polynomials and Ring of Polynomial Functions
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Graduate Maximal ideal (x,y) - and then primary ideal (x,y)^n
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Graduate Analytic expression to find the range of non-negative numbers in array
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Graduate 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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Graduate 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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Graduate Proving Primary Ideals in \mathbb{Z}: Peter's Challenge
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MHB Eigenvector and eigenvalue for differential operator
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Undergrad Newbie question: Algebra of Mahalanobis distance
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Graduate 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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Undergrad Simple conceptual misunderstanding
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MHB Reducing Quadratic Form to Principle Axes
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Graduate Primary Ideals, prime ideals and maximal ideals - D&F Section 15.2
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Graduate Isomorphic Finite Dimensional Vector Spaces
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Undergrad Simple question about parametric equations of a plane in 3D
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Graduate Affine Varieties - the x-axis in R^2
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Graduate Primary Ideals, prime ideals and maximal ideals.
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Graduate Is SO(2) Considered a Lie Group?
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MHB If a and b are unit vectors....
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MHB How Do You Invert This 2x2 Matrix?
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Graduate Proving Convexity of a Set: A Proof by Contradiction Approach
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Graduate Affine Varieties - Single Points and maximal ideals
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Undergrad Matrix transformations and effects on the unit square
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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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High School What is the notation for the distance between two position vectors?
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MHB Indexes of inertia for the function
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Graduate 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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Undergrad Different Versions of a Plane in R^3 (The Plane, The Plane)
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Undergrad 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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Graduate Algebriac Geometry - Morphisms of Algebraic Sets
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