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

Graduate Linear Programming - satisfaction only at least one constraint

  • wavingerwin
  • · Replies 4 ·
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4

Identities of the optimal approximation

  • mathmari
  • · Replies 9 ·
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9

Undergrad Help with matrix form of the imaginary unit, i

  • powerof
  • · Replies 1 ·
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1

Graduate (Non)Isomorphism of V with V** in Infinite-Dimension Case

  • WWGD
  • · Replies 15 ·
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15

Graduate What does it mean to say that something "is a gauge theory"?

  • questioner1
  • · Replies 4 ·
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4

What is the name of this theorem in Abstract Algebra

  • Amer
  • · Replies 5 ·
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5

Graduate Why Are the Eigenvalues of This Matrix A and A + φ²B?

  • Gianfelici
  • · Replies 4 ·
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4

Graduate Eigenvalues / Eigenvectors relationship to Matrix Entries Values

  • jorgejgleandro
  • · Replies 5 ·
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5

Undergrad Vector Summing in Physics: Understanding the Mathematical Rules and Exceptions

  • mech-eng
  • · Replies 9 ·
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9

Graduate Verifying that a matrix T represents a projection operation

  • Seydlitz
  • · Replies 3 ·
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3

Graduate Expected Value Partial Trance Density Matrix

  • VVS
  • · Replies 3 ·
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3

Graduate Relation between unit tangent/normal vectors, curvature, and Lin. Alg.

  • ModestyKing
  • · Replies 2 ·
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2

Why aren't there coprime integers?

  • evinda
  • · Replies 4 ·
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4

Understanding Orthogonality in Inner Product Spaces

  • mathmari
  • · Replies 2 ·
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2

Graduate Galois Theory, Differential Equations, and Lie Groups?

  • "pi"mp
  • · Replies 1 ·
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1

Functions that are injective but not surjective

  • Math Amateur
  • · Replies 5 ·
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5
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2

Graduate What are Symmetric Functions for Polynomial Roots?

  • Jhenrique
  • · Replies 2 ·
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2

Undergrad Interpolation with 2 variables

  • Jhenrique
  • · Replies 2 ·
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2

Graduate Ideal of an inversable triangular matrix

  • karin
  • · Replies 1 ·
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1

Graduate Function of operators. Series, matrices.

  • LagrangeEuler
  • · Replies 17 ·
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17

Definition of epimorphism and equivalence to 'surjectivity'

  • Math Amateur
  • · Replies 7 ·
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7

Find Sample Solutions for Underdetermined Systems of Linear Equations

  • ztepman
  • · Replies 1 ·
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1

Graduate How do you reduce a matrix with unknown components?

  • Hertz
  • · Replies 2 ·
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2

Graduate Inverse of a special matrix of arbitrary size

  • stormyweathers
  • · Replies 3 ·
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3

Undergrad Why Does Adding Two Polynomials from a Set Not Always Result in a Vector Space?

  • kq6up
  • · Replies 18 ·
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18

Undergrad Wronskian vs. Determinant in Determining Linear Independence?

  • kq6up
  • · Replies 2 ·
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2

A theorem on Quadratic Forms in Reid's Book not at all clear.

  • caffeinemachine
  • · Replies 6 ·
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6

Undergrad Condition for a number to be a Fibonacci one

  • muzialis
  • · Replies 14 ·
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14

Undergrad Is There a Formula for Unit Eigenvectors?

  • Jhenrique
  • · Replies 12 ·
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12

What are the functions of a graph in relation to arrow composition?

  • Math Amateur
  • · Replies 2 ·
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2

What Is the Universal Mapping Property in Free Monoids According to Awodey?

  • Math Amateur
  • · Replies 8 ·
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8

Graduate Tensors of Free Groups and Abelian groups

  • WWGD
  • · Replies 2 ·
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2

Abstract Algebra Sylow Subgroup

  • DavidL
  • · Replies 5 ·
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5

Solving linear equation application

  • paulmdrdo1
  • · Replies 6 ·
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6

Graduate Is A^k a Projection Operator if k is Even/Odd?

  • LagrangeEuler
  • · Replies 2 ·
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2

Is a Latin Square always invertible?

  • Sudharaka
  • · Replies 1 ·
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1

Graduate Commutator of a group is identity?

  • Kanchana
  • · Replies 3 ·
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3

Undergrad How to Mathematically describe a plane?

  • HMPARTICLE
  • · Replies 3 ·
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3

Undergrad Diagonalizing a Matrix A: The Definition and Process Explained

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Defining Functions on Tensor Products

  • WWGD
  • · Replies 7 ·
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7

Graduate Why is the Cayley-Hamilton theorem important for matrices?

  • negation
  • · Replies 2 ·
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2

Graduate Newton's identities and matrices

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Fourier Transform, Discrete Forier Transform image processing

  • joshthekid
  • · Replies 3 ·
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3

Graduate Is G/H Always an Abelian Group if H is Normal in G?

  • Kanchana
  • · Replies 1 ·
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1

Category Theory - Definition of Hom(X,X) in Awodey

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Can I Write a Hermitian Matrix as A=A^(1/2)AH^(1/2)?

  • EngWiPy
  • · Replies 4 ·
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4

Graduate What Kind of Tensor Product is v=S:∇I?

  • jure
  • · Replies 4 ·
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4

Is My Solution to the Complex Algebraic Expression Correct?

  • mathdrama
  • · Replies 3 ·
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3

Quotient rings and homorphic images

  • simo1
  • · Replies 3 ·
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3

D&F, Ch 10, Proposition 30 - Proof that (3) ===> (4)

  • Math Amateur
  • · Replies 3 ·
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3

Graduate How write a matrix in terms of determinant and trace?

  • Jhenrique
  • · Replies 5 ·
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5

Simple question of interpretation - D&F Ch 10 - Proposition 30

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Simple question of interpretation - D&F Ch 10 - Proposition 30

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Why is Understanding Column Space and Null Space Important in Linear Algebra?

  • Muthumanimaran
  • · Replies 2 ·
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2

Undergrad Matrix Rank: Meaning, Importance & What It Tells You

  • Muthumanimaran
  • · Replies 1 ·
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1

Undergrad Possibly silly linear algebra question

  • sokrates
  • · Replies 2 ·
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2

Undergrad Help with linear transformation problem with variables

  • stonecoldgen
  • · Replies 6 ·
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6

Exact Sequences - Dummit and Foote Ch 10 - Proposition 29

  • Math Amateur
  • · Replies 6 ·
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6

Graduate What Are the Automorphisms of Z[x]?

  • SS521
  • · Replies 1 ·
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1

How do I Find the Vector Coordinates to Solve for Trihedral Angle?

  • Julian1
  • · Replies 1 ·
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1

Undergrad How to solve a system with more unknowns than equations?

  • stonecoldgen
  • · Replies 1 ·
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1

Does (ab)^n Always Equal a^n*b^n in an Abelian Group?

  • evinda
  • · Replies 1 ·
Replies
1

Exact Sequences - Dummit and Foote Ch 10 - Proposition 28

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Yaw,Pitch and Roll Multiplication

  • abubakr
  • · Replies 4 ·
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4

Graduate Demonstrating that a mapping is injective

  • Math Amateur
  • · Replies 1 ·
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1

How can I find the kernel of a homomorphism of finite groups?

  • onie mti
  • · Replies 5 ·
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5

Demonstrating that a mapping is injective

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Artin's lemma in Galois Theory: when is [E:F] < |G|?

  • Boorglar
  • · Replies 2 ·
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2

How Do You List Elements of G/H in Z10 When H={α,β,δ}?

  • simo1
  • · Replies 3 ·
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3

Graduate Rate-of-strain tensor in cylindrical coords.

  • JoutlawPhysics
  • · Replies 4 ·
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4

Understanding Finite Quotient Groups: G/H with G=Z6 and H=(0,3)

  • onie mti
  • · Replies 2 ·
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2

Exact Sequences - Lifting Homomorphisms - D&F Ch 10 - Theorem 28

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Exact Sequences - Lifting Homomorphisms - D&F Ch 10 - Theorem 28

  • Math Amateur
  • · Replies 4 ·
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4

Direct Products of Modules - Bland - Rings and Their Modules

  • Math Amateur
  • · Replies 14 ·
Replies
14

Proof that Ha=Hb: Element y in Hb Proven True for Ha

  • onie mti
  • · Replies 4 ·
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4

Graduate Eigenvalue, Eigenvector and Eigenspace

  • negation
  • · Replies 6 ·
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6

Using dihedral group in Lagrange theorem

  • onie mti
  • · Replies 5 ·
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5

Graduate (Apparently) simple question rearding module homomorphisms

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Do All Subspaces in Rn Have Orthonormal Bases?

  • fredrogers3
  • · Replies 2 ·
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2

How to Solve Condition Number and LU Decomposition Problems?

  • akerman
  • · Replies 3 ·
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3

Exact Sequences - extending or lifting homomorphisms

  • Math Amateur
  • · Replies 1 ·
Replies
1

(Apparently) simple question rearding module homomorphisms

  • Math Amateur
  • · Replies 1 ·
Replies
1

Split Sequences - D&F Ch 10 Section 10.5

  • Math Amateur
  • · Replies 2 ·
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2

Help with Vector Questions in a Cartesian Coordinate System

  • paulmdrdo1
  • · Replies 7 ·
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7

Why can we show that an other polynomial is irreducible?

  • evinda
  • · Replies 2 ·
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2

Polynomial Divisibility Problem: Proof & Corollary

  • kaliprasad
  • · Replies 1 ·
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1

Proving Lagrange Theorem for Finite Group G

  • onie mti
  • · Replies 2 ·
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2

Graduate Prove that U_{m/n_1} (m) ,U_{m/n_k} (m) are normal subgroups

  • vish_maths
  • · Replies 2 ·
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2

Undergrad Vector component in different co ordinate system

  • darwined
  • · Replies 9 ·
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9

Graduate Why is q=0 for Simple Roots in Lie Algebras?

  • spookyfish
  • · Replies 4 ·
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4

Graduate Direct Products of Modules - Bland - Proposition 2.1.1 and its proof

  • Math Amateur
  • · Replies 9 ·
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9

Direct Products of Modules - Bland - Proposition 2.1.1 and its proof

  • Math Amateur
  • · Replies 6 ·
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6

Basis of a vector space - apparently simple problem

  • Math Amateur
  • · Replies 4 ·
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4

Basic Question on Modules - Dummit and Foote Chapter 10

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Rotation and translation of basis to remove cross terms

  • cooev769
  • · Replies 2 ·
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2

Graduate Direct Products of Modules - Bland - Rings and Their Modules

  • Math Amateur
  • · Replies 2 ·
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2

Graduate What is Known About Zero-th Gaussian Periods of Type (N,r)?

  • burritoloco
  • · Replies 1 ·
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1
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2

Graduate For every positive integer n there is a unique cyclic group of order n

  • BomboshMan
  • · Replies 6 ·
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6