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.
Threads
Sizes of kernels of homomorphisms
- kalish1
- · Replies 1 ·
Is the variety Z(xy - z) isomorphic to A²?
- Math Amateur
- · Replies 1 ·
Parametrization of a Reduced Matrix
- Jundoe
- · Replies 2 ·
Graduate Why is det(A)≠0 an open condition for matrix groups?
- gentsagree
- · Replies 6 ·
Partial Derivatives of Matrix/Vector Function: An Easier Way?
- datahead8888
- · Replies 1 ·
Graduate Abstract algebra: elements of fiber writable as
- HJ Farnsworth
- · Replies 2 ·
Graduate Difference between line vector and free vector
- mytch
- · Replies 3 ·
Graduate Is R/kZ under multiplication a field?
- Mandelbroth
- · Replies 5 ·
Graduate Why ||Tv||² = ||T*v||² for normal operators
- TheOldHag
- · Replies 7 ·
How Do You Convert Expressions into Bilinear Form?
- Sudharaka
- · Replies 8 ·
Dummit and Foote - Definition of Zn - Motivation?
- Math Amateur
- · Replies 4 ·
Graduate Lectures on Rings: Galois Theory
- Tenshou
- · Replies 3 ·
Graduate Does a Group Action Always Use the Group's Original Operation?
- Bachelier
- · Replies 3 ·
Graduate Why Doesn't the Tensor Identity Work Out?
- QuickLoris
- · Replies 1 ·
Graduate Is the other Gram-Schmidt process truly different from the usual one?
- Avatrin
- · Replies 2 ·
Graduate Are functionals and operators the same thing?
- gentsagree
- · Replies 3 ·
Can You Find a Counterexample for This Module Over a Commutative Ring?
- Siron
- · Replies 5 ·
Existence of a Basis of a Vector Space
- toni07
- · Replies 3 ·
Undergrad What is the difference between a field a subfield
- student34
- · Replies 6 ·
Graduate Irreducible central elements generate maximal ideals?
- Silversonic
- · Replies 1 ·
Keller industries profits system of equations
- notgoodatmath
- · Replies 3 ·
Undergrad Understanding Gauss-Jordan Method for Solving Equations
- alnix
- · Replies 1 ·
Verifying Answers to True/False Questions about Matrices
- Yankel
- · Replies 3 ·
Finding Solutions for a System of Linear Equations with 2 Degrees of Freedom
- Yankel
- · Replies 1 ·
Canonical Isomorphism and Tensor Products
- Sudharaka
- · Replies 4 ·
Understanding Tensors: Finding the Value of a Tensor
- Sudharaka
- · Replies 4 ·
Exterior Power of Linear Transformation
- Sudharaka
- · Replies 1 ·
Direct Products and Quotient Groups
- Math Amateur
- · Replies 13 ·
Prove the following; (vector spaces and linear operators)
- toni07
- · Replies 1 ·
Expressing elements of quotient group D_16/<r^4> as \overline{s}^a\overline{r}^b
- Math Amateur
- · Replies 12 ·
Graduate Triangle Inequality in 'Linear Algebra Done Right'
- TheOldHag
- · Replies 6 ·
Undergrad Does cosine similarity need absolute value for opposite vectors?
- daveronan
- · Replies 3 ·
Solving for $F(v,f)$ in Tensor $F$
- smile1
- · Replies 2 ·
Solution: What is Decomposable Tensor?
- Sudharaka
- · Replies 4 ·
Graduate Conveying inner product with words
- qubyte
- · Replies 3 ·
Undergrad Are complex numbers vectors if multiplication doesn't work like vector multiplication?
- 7777777
- · Replies 19 ·
Undergrad Systems of equations with many equations, more than 3
- Crazyhorse2882
- · Replies 1 ·
Graduate Multiplication bloards after factorization
- yiorgos
- · Replies 2 ·
Undergrad Are matrix diagonalization and eigen decomposition the same thing?
- NATURE.M
- · Replies 2 ·
Undergrad Mean value(centroid) of a collection of vectors
- daveronan
- · Replies 2 ·
Graduate How Can Tensor Decomposition Be Achieved Using Linear Methods?
- Jhenrique
- · Replies 9 ·
Graduate Why is the Binomial Formula a Derivation?
- Tenshou
- · Replies 13 ·
Graduate Ambiguity in the term 'dimension'?
- dexterdev
- · Replies 2 ·
Graduate How to find the manifold associated with a Lie Group?
- mnb96
- · Replies 7 ·
Orientation-preserving isometry of R^n
- kalish1
- · Replies 1 ·
Transforming a Linear Transformation Matrix to an Orthonormal Basis
- Sudharaka
- · Replies 11 ·
Group structure on a sphere with stereographic projection
- mathbalarka
- · Replies 13 ·
Undergrad Span of a Set of Linear Transformations
- jsgoodfella
- · Replies 2 ·
Finding GCD in Gaussian Integers
- ArcanaNoir
- · Replies 3 ·
Uniquely Determined Linear Operator
- Sudharaka
- · Replies 7 ·
Permutation representation argument validity
- kalish1
- · Replies 7 ·
Let f(x) = x^2 + 1 and g(x) = x^3 + 1.
- toni07
- · Replies 7 ·
Undergrad What is the difference between inner product and dot product?
- Jhenrique
- · Replies 3 ·
Classifying quadratic surfaces using eigenvalues of A
- FilipVz
- · Replies 1 ·
Graduate Difference between the A conjugate and A dagger
- Hazzattack
- · Replies 4 ·
Undergrad Determinants between two similar matrices
- NATURE.M
- · Replies 4 ·
Graduate Two linear transformations agree, subspace
- 1MileCrash
- · Replies 10 ·
Graduate Cartesian Product of Permutations?
- Parmenides
- · Replies 1 ·
Undergrad Explain why matrix multiplication is not commutative.
- xsgx
- · Replies 4 ·
Graduate Ring of Polynomials and Ring of Polynomial Functions
- Mandelbroth
- · Replies 5 ·
Graduate Why is (x,y)^n primary in k[x,y]?
- Math Amateur
- · Replies 4 ·
Graduate Analytic expression to find the range of non-negative numbers in array
- nazmul.islam
- · Replies 2 ·
Graduate Creating a matrix with desirable eigenvalues
- Deimantas
- · Replies 7 ·
How to Find \(a^2\) from a Matrix Inverse Equation?
- Yankel
- · Replies 5 ·
Primary Ideals, prime ideals and maximal ideals.
- Math Amateur
- · Replies 1 ·
Finding element of inverse matrix
- Yankel
- · Replies 2 ·
Maximal ideal (x,y) - and then primary ideal (x,y)^n
- Math Amateur
- · Replies 13 ·
Normal Form and Canonical Form of a Quadratic
- Sudharaka
- · Replies 20 ·
Orthogonal Transformation in Euclidean Space
- Sudharaka
- · Replies 5 ·
Stabilizer subgroups - proof verification
- kalish1
- · Replies 2 ·
Surjectivity for permutation representation of a group action
- kalish1
- · Replies 2 ·
Is the Ideal (x) in k[x, y] a Prime Ideal?
- Math Amateur
- · Replies 3 ·
Graduate Why is (x) a prime ideal in k[x,y]?
- Math Amateur
- · Replies 2 ·
Is the Projection Operator Self-Adjoint Only with Orthogonal Subspaces?
- smile1
- · Replies 1 ·
Why is (4) not a primary ideal in ℤ?
- Math Amateur
- · Replies 8 ·
Canonical Basis and Standard Basis
- Sudharaka
- · Replies 9 ·
How Can I Visualize a $\pi/2$ Rotation About $(1,1,0)^t$ in $\mathbb{R}^3$?
- kalish1
- · Replies 3 ·
Graduate Proving Primary Ideals in \mathbb{Z}: Peter's Challenge
- Math Amateur
- · Replies 2 ·
Eigenvector and eigenvalue for differential operator
- kalish1
- · Replies 4 ·
Undergrad Newbie question: Algebra of Mahalanobis distance
- anja.ende
- · Replies 3 ·
Graduate What is the volume of these special n-dimensional ellipsoids?
- jstar
- · Replies 1 ·
Why is rad M = M when M is a maximal ideal?
- Math Amateur
- · Replies 2 ·
Undergrad Simple conceptual misunderstanding
- jaydnul
- · Replies 3 ·
Reducing Quadratic Form to Principle Axes
- Sudharaka
- · Replies 6 ·
Graduate Why rad M = M when M is a maximal ideal
- Math Amateur
- · Replies 4 ·
Graduate Isomorphic Finite Dimensional Vector Spaces
- TheOldHag
- · Replies 5 ·
Undergrad Parametric equations for the plane z=2
- ainster31
- · Replies 5 ·
Graduate Affine Varieties - the x-axis in R^2
- Math Amateur
- · Replies 1 ·
Graduate Primary Ideals, prime ideals and maximal ideals.
- Math Amateur
- · Replies 1 ·
Graduate Is SO(2) Considered a Lie Group?
- mnb96
- · Replies 16 ·
Finding (2a-b)·(a+3b) when a and b are unit vectors
- Raerin
- · Replies 3 ·
How Do You Invert This 2x2 Matrix?
- ends
- · Replies 6 ·
Graduate Proving Convexity of a Set: A Proof by Contradiction Approach
- TaPaKaH
- · Replies 2 ·
Graduate Affine Varieties - Single Points and maximal ideals
- Math Amateur
- · Replies 2 ·
Undergrad Matrix transformations and effects on the unit square
- fogvajarash
- · Replies 3 ·
Questions about Jordan Normal Form
- Sudharaka
- · Replies 9 ·
Mapping and inverse mapping of open sets and their complements
- alyafey22
- · Replies 1 ·
High School What is the notation for the distance between two position vectors?
- CraigH
- · Replies 4 ·
Indexes of inertia for the function
- smile1
- · Replies 1 ·
Graduate Spinor representations decomposed under subgroups in Joe's big book
- whitejet
- · Replies 3 ·