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

Minimal polynomial of e^(2πi/3) + ∛2 over ℚ

  • kalish1
  • · Replies 1 ·
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1

Graduate Symmetry of Orthogonally diagonalizable matrix

  • DmytriE
  • · Replies 6 ·
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6

Undergrad Linear Combination Mapping: Is the Invertible Matrix Theorem True or False?

  • henry3369
  • · Replies 5 ·
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5

Graduate Can the Set R(G) be Proven as a Ring in Convolution on Groups?

  • Bipolarity
  • · Replies 1 ·
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1

Graduate Vector subspace and linear transformation

  • Montgomery
  • · Replies 1 ·
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1

Homomorphism - Sharper Cayley Theorem

  • Kiwi1
  • · Replies 3 ·
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3

Finding Isomorphisms between Groups: D6, A4, S3xZ2, G

  • Enzipino
  • · Replies 1 ·
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1

Graduate Book for abstract algebra (group and galois theory)

  • Avatrin
  • · Replies 4 ·
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4

Graduate Proof that eigenvalues are constants

  • jk22
  • · Replies 7 ·
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7

Could you explain me about 'relation algebraic property with conjugate'?

  • bw0young0math
  • · Replies 2 ·
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2

Undergrad Complex numbers and vector multiplies continued

  • keldon
  • · Replies 15 ·
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15

Graduate Relationship between inverse matrix and inertia tensor?

  • Bruno Tolentino
  • · Replies 2 ·
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2

Determinant - Proof for distinct real numbers

  • Dethrone
  • · Replies 2 ·
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2

Proof: Determinant of 3 Non-Colinear Points is 0

  • Dethrone
  • · Replies 5 ·
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5

What is Algebraic Multiplicity and How Does It Relate to Solving Matrices?

  • Dethrone
  • · Replies 20 ·
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20

What is the basis for $F$ in linear algebra?

  • Dethrone
  • · Replies 2 ·
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2

Finding a basis for a Vector Space

  • Dethrone
  • · Replies 3 ·
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3

Graduate Why does this shortcut for eigenvectors of 2x2 symmetric work?

  • RickF-
  • · Replies 1 ·
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1

Graduate Scaling the parameter of the SO(2) rotation matrix

  • spaghetti3451
  • · Replies 2 ·
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2

Graduate Representations of semi-simple lie algebra

  • branch
  • · Replies 7 ·
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7

Graduate Computing the Inverse of a Cubic Matrix

  • Bruno Tolentino
  • · Replies 4 ·
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4

Squares in a field with q^n elements

  • Prefer
  • · Replies 3 ·
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3

Graduate Large weighted least squares system

  • vibe3
  • · Replies 4 ·
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4

Graduate Vector Identity: Understanding ∇⋅A and A ⋅∇ in Spherical Coordinates

  • majormuss
  • · Replies 7 ·
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7

Undergrad Matrix Differentiation Problem

  • leonmate
  • · Replies 3 ·
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3

Undergrad Are a billion 3's in a row contained in pi's digits?

  • rmberwin
  • · Replies 24 ·
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24

Undergrad 4th order Polynomail starting at a desired Point

  • mrmonk7663
  • · Replies 16 ·
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16

Graduate Jacobi and Gauss-Seidel Iteration

  • nxtgarnett
  • · Replies 1 ·
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1

Undergrad How to find a point on line of intersection of 2 planes?

  • NotASmurf
  • · Replies 9 ·
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9

Fourth degree polynomial with zeros at ±2 and ±3i

  • kelly
  • · Replies 5 ·
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5

Graduate Transforming Vectors from Basis B to C: A Confusing Matter

  • devd
  • · Replies 3 ·
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3

Vector that describes the power

  • mathmari
  • · Replies 18 ·
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18

Find the minimal polynomial of some value a over Q

  • E01
  • · Replies 1 ·
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1

Graduate Algebraic Multiplicity of an Eigenvalue

  • vish_maths
  • · Replies 4 ·
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4

Graduate A lemma in proving Sylow's theorem

  • Bipolarity
  • · Replies 1 ·
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1

Show eigenvalues are real and positive (too easy?)

  • ognik
  • · Replies 2 ·
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2

Can a vector space also be a set?

  • ognik
  • · Replies 3 ·
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3

Undergrad How Did Abstract Algebra Evolve From Elementary Algebra?

  • Avichal
  • · Replies 1 ·
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1

One-to-one correspondence between conjugates of H and cosets of N

  • Kiwi1
  • · Replies 1 ·
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1

What is the General Pattern for Finding Matrix Powers?

  • Aryth1
  • · Replies 2 ·
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2

Graduate Why do 2-tensors and linear maps both correspond to n×n matrices?

  • JonnyG
  • · Replies 10 ·
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10

Graduate Why does f(x) = f(x₁i + x₂j + x₃k) in theorem 4.2.5?

  • PcumP_Ravenclaw
  • · Replies 2 ·
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2

Graduate Operator measuring distinctness of superposition components

  • Agrippa
  • · Replies 12 ·
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12

Antisymmetry Invariant Under Similarity Orthogonal Transforms

  • ognik
  • · Replies 3 ·
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3

Product of Symmetric and Antisymmetric Matrix

  • ognik
  • · Replies 2 ·
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2
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5

Graduate Can the system response function be calculated?

  • Adel Makram
  • · Replies 11 ·
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11

Graduate Two quotient groups implying Cartesian product?

  • jostpuur
  • · Replies 2 ·
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2

Question about the "E" Lie algebras

  • topsquark
  • · Replies 0 ·
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0

Undergrad Eigenvalues and diagonalization of a matrix

  • dyn
  • · Replies 4 ·
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4
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2

Graduate Least Square Estimator for Matrices: Bill's Problem

  • bhobba
  • · Replies 5 ·
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5

Undergrad How Does the Vector Field F = [-x³, x, 0] Behave for Constant x Values?

  • uzman1243
  • · Replies 13 ·
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13

Undergrad Solving x + (x · a)c = b with vector equation doubts

  • PcumP_Ravenclaw
  • · Replies 3 ·
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3

What Are the Bases for Column and Null Spaces of These Matrices?

  • aidandeno
  • · Replies 1 ·
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1

Direct sum of p-primary components of an R-module counterexample?

  • kalish1
  • · Replies 1 ·
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1

Graduate Solution to vector equation involving vector product

  • PcumP_Ravenclaw
  • · Replies 19 ·
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19

Undergrad What is the necessary condition for matrix commutation?

  • fairy._.queen
  • · Replies 6 ·
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6

Graduate Finding the points of a cube given two points.

  • ilikeintegrals
  • · Replies 1 ·
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1

Inverse image of a set under the restriction of a function

  • Math Amateur
  • · Replies 2 ·
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2

Proving elipsoide radius of axis i equals 1/sqrt(λi)

  • JanezK
  • · Replies 2 ·
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2

Proving that a module can be decomposed as a direct sum of submodules

  • kalish1
  • · Replies 1 ·
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1

Graduate When n*(n+1)/2 - k is never a square

  • OlderOwl
  • · Replies 2 ·
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2

Why are 4-cycles, 3-cycles, and 5-cycles not in A₅?

  • Enzipino
  • · Replies 1 ·
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1

Finding inverse of F in Munkres' Topology Ch.2 EX 5 pg 106

  • Math Amateur
  • · Replies 2 ·
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2

Graduate What does it mean to say a Lie group is real?

  • pellman
  • · Replies 2 ·
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2

Definition of matrix transformation

  • Carla1985
  • · Replies 3 ·
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3

Graduate Matrix notation for gradient of vector field applied to vector

  • aaaa202
  • · Replies 2 ·
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2

Relation between null and column space

  • Dethrone
  • · Replies 3 ·
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3

Eigenvector of 3x3 matrix with complex eigenvalues

  • rayne1
  • · Replies 1 ·
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1

Injective and surjective functions

  • Ciaran
  • · Replies 12 ·
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12

General orthogonal scale factor identity

  • ognik
  • · Replies 1 ·
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1

Undergrad Looking for an example of a Successive over-relaxation

  • hahaha158
  • · Replies 10 ·
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10

Graduate Why Doesn't This Theorem Hold in Real Vector Spaces?

  • dyn
  • · Replies 13 ·
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13

Basis for $U$ using $\operatorname{null}A$

  • Dethrone
  • · Replies 2 ·
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2

Undergrad System of homogeneous equations

  • AdityaDev
  • · Replies 3 ·
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3

Graduate Is sl(3,R) a subalgebra of sp(4,R)?

  • Kurret
  • · Replies 1 ·
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1

Undergrad Euler's identity, mathematical beauty and applications of it

  • audire
  • · Replies 4 ·
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4
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6

Undergrad How to Solve Equations with a Singular Matrix?

  • nelectrode
  • · Replies 3 ·
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3
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3

Why Is My Determinant Calculation Using Upper Triangular Form Incorrect?

  • Dethrone
  • · Replies 3 ·
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3

Graduate How Do You Find a Basis for the Orthogonal Complement of Given Vectors in ℝ5?

  • ichabodgrant
  • · Replies 8 ·
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8

Showing ker A = 0 for dual tensor product to multilinear forms map

  • caffeinemachine
  • · Replies 3 ·
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3

Graduate Block diagonalization of a matrix

  • Qturtle
  • · Replies 1 ·
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1

High School Proof of (A+B)^2 = A^2 + 2AB + B^2 for Matrix Algebra

  • Kavorka
  • · Replies 4 ·
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4

Undergrad Test Tomorrow Linear independence, spanning, basis

  • blakpete91
  • · Replies 7 ·
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7
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2

Undergrad Understand Linear Algebra: Im(BF) in Im(B)?

  • Payam30
  • · Replies 3 ·
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3

High School Difference between REF/RREF (Gauss vs Gauss-Jordan)?

  • leo255
  • · Replies 1 ·
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1

Barycentric coordinates in a triangle - proof

  • Samwise1
  • · Replies 5 ·
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5

Graduate Coefficients on the p-adic expansions

  • MostlyHarmless
  • · Replies 1 ·
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1

Graduate P-adic norm, valuation, and expansion

  • MostlyHarmless
  • · Replies 1 ·
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1

Graduate Properties of iterated Cholesky decomposition products

  • amateur82
  • · Replies 1 ·
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1

Graduate How to Simplify a Double Dot Product of Tensors?

  • nikphd
  • · Replies 5 ·
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5

Graduate Constructing a field of 4 elements

  • PsychonautQQ
  • · Replies 4 ·
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4

Graduate Su(2), so(3) and their representations

  • Lapidus
  • · Replies 2 ·
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2

Undergrad QR Decomposition w/ Householder and Givens Transformations

  • Th3HoopMan
  • · Replies 4 ·
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4

Graduate Double Dot Product: Solving 3D Vector Problem

  • Naake
  • · Replies 3 ·
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3