Linear and Abstract Algebra Forum

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

Parametrization of a Reduced Matrix

  • Jundoe
  • · Replies 2 ·
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2

Graduate Open Conditions for Matrix Groups: Understanding the Role of det(A)≠0

  • gentsagree
  • · Replies 6 ·
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6

Partial Derivatives of Matrix/Vector Function: An Easier Way?

  • datahead8888
  • · Replies 1 ·
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1

Graduate Abstract algebra: elements of fiber writable as

  • HJ Farnsworth
  • · Replies 2 ·
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2

Graduate Difference between line vector and free vector

  • mytch
  • · Replies 3 ·
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3

Graduate Is R/kZ under multiplication a field?

  • Mandelbroth
  • · Replies 5 ·
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5

Graduate Understanding the Normal Operator Equality in Proofs of Properties

  • TheOldHag
  • · Replies 7 ·
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7

How Do You Convert Expressions into Bilinear Form?

  • Sudharaka
  • · Replies 8 ·
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8

Dummit and Foote - Definition of Zn - Motivation?

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Lectures on Rings: Galois Theory

  • Tenshou
  • · Replies 3 ·
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3

Graduate Does a Group Action Always Use the Group's Original Operation?

  • Bachelier
  • · Replies 3 ·
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3

Graduate Why Doesn't the Tensor Identity Work Out?

  • QuickLoris
  • · Replies 1 ·
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1

Graduate Is the other Gram-Schmidt process truly different from the usual one?

  • Avatrin
  • · Replies 2 ·
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2

Graduate Are functionals and operators the same thing?

  • gentsagree
  • · Replies 3 ·
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3

Can You Find a Counterexample for This Module Over a Commutative Ring?

  • Siron
  • · Replies 5 ·
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5

Existence of a Basis of a Vector Space

  • toni07
  • · Replies 3 ·
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3

Undergrad What is the difference between a field a subfield

  • student34
  • · Replies 6 ·
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6

Graduate Irreducible central elements generate maximal ideals?

  • Silversonic
  • · Replies 1 ·
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1

Help with system of equations: using profits

  • notgoodatmath
  • · Replies 3 ·
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3

Undergrad Understanding Gauss-Jordan Method for Solving Equations

  • alnix
  • · Replies 1 ·
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1

Verifying Answers to True/False Questions about Matrices

  • Yankel
  • · Replies 3 ·
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3
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1

Canonical Isomorphism and Tensor Products

  • Sudharaka
  • · Replies 4 ·
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4

Understanding Tensors: Finding the Value of a Tensor

  • Sudharaka
  • · Replies 4 ·
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4

Exterior Power of Linear Transformation

  • Sudharaka
  • · Replies 1 ·
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1

Direct Products and Quotient Groups

  • Math Amateur
  • · Replies 13 ·
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13

Prove the following; (vector spaces and linear operators)

  • toni07
  • · Replies 1 ·
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1

Quotient Groups - Dummit and Foote, Section 3.1, Exercise 17

  • Math Amateur
  • · Replies 12 ·
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12

Graduate Triangle Inequality in 'Linear Algebra Done Right'

  • TheOldHag
  • · Replies 6 ·
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6

Undergrad Cosine Similarity: Explained and Examples

  • daveronan
  • · Replies 3 ·
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3

Solving for $F(v,f)$ in Tensor $F$

  • smile1
  • · Replies 2 ·
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2

Solution: What is Decomposable Tensor?

  • Sudharaka
  • · Replies 4 ·
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4

Graduate Conveying inner product with words

  • qubyte
  • · Replies 3 ·
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3

Undergrad Complex Numbers as Vectors: An Exploration of Their Properties and Applications

  • 7777777
  • · Replies 19 ·
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19

Undergrad Systems of equations with many equations, more than 3

  • Crazyhorse2882
  • · Replies 1 ·
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1

Graduate Multiplication bloards after factorization

  • yiorgos
  • · Replies 2 ·
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2

Undergrad Matrix Diagonalization & Eigen Decomposition

  • NATURE.M
  • · Replies 2 ·
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2

Undergrad Mean value(centroid) of a collection of vectors

  • daveronan
  • · Replies 2 ·
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2

Graduate How Can Tensor Decomposition Be Achieved Using Linear Methods?

  • Jhenrique
  • · Replies 9 ·
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9

Graduate Why is the Binomial Formula a Derivation?

  • Tenshou
  • · Replies 13 ·
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13

Graduate Ambiguity in the term 'dimension'?

  • dexterdev
  • · Replies 2 ·
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2

Graduate How to find the manifold associated with a Lie Group?

  • mnb96
  • · Replies 7 ·
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7

Orientation-preserving isometry of R^n

  • kalish1
  • · Replies 1 ·
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1

Transforming a Linear Transformation Matrix to an Orthonormal Basis

  • Sudharaka
  • · Replies 11 ·
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11

Arithmetic Geometry on 2-sphere: Mordell-Weil Finiteness

  • mathbalarka
  • · Replies 13 ·
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13

Undergrad Span of a Set of Linear Transformations

  • jsgoodfella
  • · Replies 2 ·
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2

Finding GCD in Gaussian Integers

  • ArcanaNoir
  • · Replies 3 ·
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3

Uniquely Determined Linear Operator

  • Sudharaka
  • · Replies 7 ·
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7

Permutation representation argument validity

  • kalish1
  • · Replies 7 ·
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7

Let f(x) = x^2 + 1 and g(x) = x^3 + 1.

  • toni07
  • · Replies 7 ·
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7

Undergrad Inner Product vs Dot Product: Understanding the Difference

  • Jhenrique
  • · Replies 3 ·
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3
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1

Graduate Difference between the A conjugate and A dagger

  • Hazzattack
  • · Replies 4 ·
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4

Undergrad Determinants between two similar matrices

  • NATURE.M
  • · Replies 4 ·
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4

Graduate Two linear transformations agree, subspace

  • 1MileCrash
  • · Replies 10 ·
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10

Graduate Cartesian Product of Permutations?

  • Parmenides
  • · Replies 1 ·
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1

Undergrad Explain why matrix multiplication is not commutative.

  • xsgx
  • · Replies 4 ·
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4

Graduate Ring of Polynomials and Ring of Polynomial Functions

  • Mandelbroth
  • · Replies 5 ·
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5

Graduate Maximal ideal (x,y) - and then primary ideal (x,y)^n

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Analytic expression to find the range of non-negative numbers in array

  • nazmul.islam
  • · Replies 2 ·
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2

Graduate Creating a matrix with desirable eigenvalues

  • Deimantas
  • · Replies 7 ·
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7

How to Find \(a^2\) from a Matrix Inverse Equation?

  • Yankel
  • · Replies 5 ·
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5

Primary Ideals, prime ideals and maximal ideals.

  • Math Amateur
  • · Replies 1 ·
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1

Finding element of inverse matrix

  • Yankel
  • · Replies 2 ·
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2

Maximal ideal (x,y) - and then primary ideal (x,y)^n

  • Math Amateur
  • · Replies 13 ·
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13

Normal Form and Canonical Form of a Quadratic

  • Sudharaka
  • · Replies 20 ·
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20

Orthogonal Transformation in Euclidean Space

  • Sudharaka
  • · Replies 5 ·
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5

Stabilizer subgroups - proof verification

  • kalish1
  • · Replies 2 ·
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2

Surjectivity for permutation representation of a group action

  • kalish1
  • · Replies 2 ·
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2

Is the Ideal (x) in k[x, y] a Prime Ideal?

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Why is (x) a prime ideal in k[x,y]?

  • Math Amateur
  • · Replies 2 ·
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2

Is the Projection Operator Self-Adjoint Only with Orthogonal Subspaces?

  • smile1
  • · Replies 1 ·
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1

Prove Primary Ideals in \mathbb{Z}: Peter's Questions Answered

  • Math Amateur
  • · Replies 8 ·
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8

Canonical Basis and Standard Basis

  • Sudharaka
  • · Replies 9 ·
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9
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3

Graduate Proving Primary Ideals in \mathbb{Z}: Peter's Challenge

  • Math Amateur
  • · Replies 2 ·
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2

Eigenvector and eigenvalue for differential operator

  • kalish1
  • · Replies 4 ·
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4

Undergrad Newbie question: Algebra of Mahalanobis distance

  • anja.ende
  • · Replies 3 ·
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3

Graduate What is the volume of these special n-dimensional ellipsoids?

  • jstar
  • · Replies 1 ·
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1

Primary Ideals, prime ideals and maximal ideals - D&F Section 15.2

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Simple conceptual misunderstanding

  • jaydnul
  • · Replies 3 ·
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3

Reducing Quadratic Form to Principle Axes

  • Sudharaka
  • · Replies 6 ·
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6

Graduate Primary Ideals, prime ideals and maximal ideals - D&F Section 15.2

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Isomorphic Finite Dimensional Vector Spaces

  • TheOldHag
  • · Replies 5 ·
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5

Undergrad Simple question about parametric equations of a plane in 3D

  • ainster31
  • · Replies 5 ·
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5

Graduate Affine Varieties - the x-axis in R^2

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Primary Ideals, prime ideals and maximal ideals.

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Is SO(2) Considered a Lie Group?

  • mnb96
  • · Replies 16 ·
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16

If a and b are unit vectors....

  • Raerin
  • · Replies 3 ·
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3

How Do You Invert This 2x2 Matrix?

  • ends
  • · Replies 6 ·
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6

Graduate Proving Convexity of a Set: A Proof by Contradiction Approach

  • TaPaKaH
  • · Replies 2 ·
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2

Graduate Affine Varieties - Single Points and maximal ideals

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Matrix transformations and effects on the unit square

  • fogvajarash
  • · Replies 3 ·
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3

Questions about Jordan Normal Form

  • Sudharaka
  • · Replies 9 ·
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9

Mapping and inverse mapping of open sets and their complements

  • alyafey22
  • · Replies 1 ·
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1

High School What is the notation for the distance between two position vectors?

  • CraigH
  • · Replies 4 ·
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4

Indexes of inertia for the function

  • smile1
  • · Replies 1 ·
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1

Graduate Spinor representations decomposed under subgroups in Joe's big book

  • whitejet
  • · Replies 3 ·
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3
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2

Hermitian Function Proof: Correcting a Mistake

  • Sudharaka
  • · Replies 5 ·
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5