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

Modules - Northott: Proposition 1

  • Math Amateur
  • · Replies 2 ·
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2

Show that it satisfies the equation

  • mathmari
  • · Replies 12 ·
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12

Show $\|.\|$ is an Norm: Prove Triangle Inequality

  • Julio1
  • · Replies 5 ·
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5

Graduate Factor Groups: What am I thinking about wrongly here?

  • PsychonautQQ
  • · Replies 3 ·
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3

Algebraic Proofs and Verifying identities

  • abbarajum
  • · Replies 5 ·
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5

Graduate Is Matrix Addition Commutative?

  • albega
  • · Replies 4 ·
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4

High School Modulus & Division: Last Digit of Numbers Explained

  • Rishav sapahi
  • · Replies 3 ·
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3

Can every subring of an algebraic extension be a field?

  • mathmari
  • · Replies 8 ·
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8

Graduate How do I make a change of basis with tensors in multilinear algebra?

  • space-time
  • · Replies 1 ·
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1

Graduate Iterations of functions of noncommutative variables

  • hilbert2
  • · Replies 3 ·
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3

Dimension and Basis of a Relation in R5

  • Logan Land
  • · Replies 6 ·
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6

Find the coordinates of the expression

  • Logan Land
  • · Replies 4 ·
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4

Find coordinates of f′, f′′, f′′′ in the basis

  • Logan Land
  • · Replies 20 ·
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20

Showing Linearity of $\varphi$ for $K(a)$

  • mathmari
  • · Replies 5 ·
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5
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5

What Is the Splitting Field for \(x^{p^{80}}-1\) Over \(\mathbb{F}_p\)?

  • mathmari
  • · Replies 6 ·
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6

Field extensions and degree of odd prime numbers

  • mathmari
  • · Replies 6 ·
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6

Undergrad Why equating two planes does not provide solutions?

  • MathewsMD
  • · Replies 8 ·
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8

Graduate Artin - domains don't seem to match

  • Whovian
  • · Replies 1 ·
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1

Graduate Eigenstuff of Second Derivative

  • Hertz
  • · Replies 4 ·
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4

Graduate Pfaffian and determinants of skew symmetric matrices

  • camilus
  • · Replies 1 ·
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1

Undergrad Line operations on matrix products

  • gummz
  • · Replies 1 ·
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1

Undergrad Defining a vector in magnitude,angle form.

  • Hijaz Aslam
  • · Replies 1 ·
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1

Graduate Are the Functions Linearly Independent Based on the Matrix of Their Outputs?

  • Alban1806
  • · Replies 2 ·
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2

Undergrad Line of intersection of two planes

  • MarcL
  • · Replies 2 ·
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2

High School Finding determinant through Gaussian elimination

  • purplecows
  • · Replies 3 ·
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3

Graduate Solving the Inversion Problem with RGB Filters

  • Edward Zhang
  • · Replies 1 ·
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1

Graduate Is the Klein Four Group Identical to the Dihedral Group D2?

  • ChrisVer
  • · Replies 3 ·
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3

How can I prove that $\theta_p$ is a p-Norm?

  • evinda
  • · Replies 7 ·
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7

Graduate Associativity of Hadamard and matrix product

  • Zoli
  • · Replies 2 ·
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2

Graduate Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)

  • Sravoff
  • · Replies 4 ·
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4

Undergrad Why is det(C)=det(A)^(n-1) for cofactors and determinants?

  • Unusualskill
  • · Replies 1 ·
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1

Let F ={0 , 1 , a , b} be a field with four elements.

  • rayne1
  • · Replies 2 ·
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2

Undergrad Proving Non-Trivial Solutions of Ax = b

  • HaLAA
  • · Replies 3 ·
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3

Units of the set of all Eisenstein Integers

  • Math Amateur
  • · Replies 6 ·
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6

Ring of integer p-adic numbers.

  • evinda
  • · Replies 1 ·
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1

Undergrad Proving Determinant of Matrix Unchanged by Adding Columns

  • Unusualskill
  • · Replies 2 ·
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2
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1

Graduate Groups of homomorphisms of abelian groups

  • JD_Shadowplay
  • · Replies 1 ·
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1
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4

Units of the Gaussian Integers, Z[i]

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Is intuition more important than logical proof in mathematics?

  • hideelo
  • · Replies 7 ·
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7

Graduate Can you explain the determinant formula using permutation notation?

  • Unusualskill
  • · Replies 3 ·
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3

Every submodule has at least one set of generators?

  • Math Amateur
  • · Replies 7 ·
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7

Graduate Does the inverse of this special matrix have a power series expansion?

  • srz
  • · Replies 5 ·
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5

Graduate Is the Canonical Basis in Mathematics Just a Useful Convention?

  • rkaminski
  • · Replies 6 ·
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6

Graduate Properties of Kernels of Homeomorphisms

  • WWGD
  • · Replies 7 ·
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7
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4

Why must the ring $K[x]$ have infinitely many irreducible polynomials?

  • mathmari
  • · Replies 7 ·
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7

Undergrad Transform Cylindrical coordinates into Cartesian Coordiantes

  • kexanie
  • · Replies 3 ·
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3

The polynomial is irreducible iff the condition is satisfied

  • mathmari
  • · Replies 3 ·
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3

Graduate Explicit construction of isomorphisms of low-rank Lie algebras.

  • lpetrich
  • · Replies 2 ·
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2

Problem Regarding Left Unital Artinian Ring (set by Euge)

  • Math Amateur
  • · Replies 3 ·
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3

Field extension-degree of the minimal polynom

  • mathmari
  • · Replies 1 ·
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1

Ordered Index Sets for Direct Sums & Products of Modules: Explained by B&K

  • Math Amateur
  • · Replies 7 ·
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7

Prove that the order of 5 modulo 2^k is 2^(k-2)

  • Fermat1
  • · Replies 8 ·
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8

Direct Sums of Copies of Modules - B&K - Exercise 2.1.6 (iii)

  • Math Amateur
  • · Replies 7 ·
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7

Show the Units of Zn with modular multiplication are a group

  • E01
  • · Replies 2 ·
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2

Finding Notation for Left Invariant Vector Fields on Lie Groups

  • topsquark
  • · Replies 3 ·
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3

Graduate Function scales eigenvalues, but what happens to eigenvectors?

  • johnpjust
  • · Replies 7 ·
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7

Undergrad Finding Inverse of Matrix by using Gaussian-Jordan Elimination

  • shuiki0306
  • · Replies 6 ·
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6

Definition of a Right Artinian Ring - Cohn - page 66

  • Math Amateur
  • · Replies 15 ·
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15

Prove that the sum is equal to -1.

  • evinda
  • · Replies 7 ·
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7

Free modules, M_n(R)-modules and M_N(R)-R-bimodules - Berrick and Keating

  • Math Amateur
  • · Replies 1 ·
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1

Infinite Direct Sums and Standard Inclusions and Projections

  • Math Amateur
  • · Replies 1 ·
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1

Direct Products and External Direct Sums

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Question about invariant w.r.t. a group action

  • mnb96
  • · Replies 3 ·
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3

Undergrad Understanding Linear Algebra Solutions: Sketching and Ratios Explained

  • woundedtiger4
  • · Replies 3 ·
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3

Graduate Compensating for Accelerometer Misalignment

  • IMK
  • · Replies 1 ·
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1

Determining if a set is a subspace.

  • AngrySnorlax
  • · Replies 4 ·
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4

Undergrad What is is neither injective, surjective, and bijective?

  • woundedtiger4
  • · Replies 9 ·
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9
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2

What Determines Group Homomorphisms Between Rational Numbers?

  • Fermat1
  • · Replies 5 ·
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5

Modules of Finite Length - Cohn, page 61

  • Math Amateur
  • · Replies 34 ·
2
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34

Generalizing Rigid Motions Group w/ Metric

  • topsquark
  • · Replies 3 ·
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3

What is the Definition of a Derivation for a Lie Algebra?

  • topsquark
  • · Replies 4 ·
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4

Undergrad Proof of R being a Vector Space - Best Resources Available

  • woundedtiger4
  • · Replies 7 ·
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7

Graduate SU(2) as a normal subgroup of SL(2, C)

  • TrickyDicky
  • · Replies 3 ·
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3

Definition of SO(n): O(n) & SL(n, \mathbb{R}) Intersection

  • topsquark
  • · Replies 1 ·
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1

Graduate Writing 3rd Order Tensor Symmetric Part in Tensor Form

  • mikeeey
  • · Replies 5 ·
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5

Graduate Are All Indecomposable Groups Cyclic?

  • metapuff
  • · Replies 4 ·
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4

Undergrad Is simultaneous row operation allowed in reducing a matrix to row echelon form?

  • MathewsMD
  • · Replies 5 ·
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5

Graduate Why Does a Functional Depend on the Curve and Its Derivative?

  • &quot;Don&#039;t panic!&quot;
  • · Replies 1 ·
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1

Undergrad Show that origin in R^n is the n-tuple 0=(0,0, .,0)

  • woundedtiger4
  • · Replies 6 ·
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6

A group of even order contains an odd number of elements of order 2

  • mathmari
  • · Replies 3 ·
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3

Looking for an online Algebra resource

  • topsquark
  • · Replies 6 ·
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6

Subnormal Series and Composition Series

  • Math Amateur
  • · Replies 6 ·
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6

Theorem on the Lengths of Modules - Cohn, Theorem 2.5

  • Math Amateur
  • · Replies 1 ·
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1

Graduate What are the algebra prerequisites for Lie groups?

  • kostas230
  • · Replies 24 ·
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24

Show that the elements have the same order

  • mathmari
  • · Replies 5 ·
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5

Verifying Sentences about Groups: Answers and Hints

  • mathmari
  • · Replies 6 ·
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6

Help Peter Prove Simple Proposition on Simple Groups & Maximal Normal Subgroups

  • Math Amateur
  • · Replies 3 ·
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3

Factor Groups and Simple Groups - Fraleigh: Theorem 15.18

  • Math Amateur
  • · Replies 1 ·
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1

Show that there are y,z such that y,z commute and their order is m and n

  • mathmari
  • · Replies 2 ·
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2

A cyclic group with only one generator can have at most two elements

  • mathmari
  • · Replies 4 ·
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4

Vector algebra- centroid of tetrahedron

  • mathisfun1
  • · Replies 3 ·
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3

Graduate Solving Doubts When Showing Simple Properties of Norms

  • dumb_curiosity
  • · Replies 7 ·
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7

Proof that covariance matrix is positive semidefinite

  • AlanTuring
  • · Replies 1 ·
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1

Undergrad Finding intersection of three planes

  • Tarrius
  • · Replies 5 ·
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5

Any1 can recommend any good e-book for linear algebra ?

  • Unusualskill
  • · Replies 5 ·
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5