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

Calculate Resultant of $g(x)=X^3+pX+q$

  • evinda
  • · Replies 5 ·
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5

Showing $XF_{X}+YF_{Y}+ZF_{Z}=nF$ with a Homogeneous Polynomial

  • evinda
  • · Replies 4 ·
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4

The Contravariant Functor Hom_R( _ , X)

  • Math Amateur
  • · Replies 2 ·
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2

Composition Series for Group Order 30

  • Pratibha
  • · Replies 4 ·
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4

Graduate 3 Dimensional Representation of D3

  • ChrisVer
  • · Replies 2 ·
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2

Irreducible polynomial/Splitting field

  • mathmari
  • · Replies 3 ·
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3

Short Five Lemma - Checking Some Simple 'Diagram Chasing'

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Basic Questions in linear algebra and group theory

  • Heisenberg1993
  • · Replies 8 ·
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8

Simple Issue of oh symbol - exact sequences

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Momentum operator in "open" space

  • ShayanJ
  • · Replies 3 ·
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3

Bilinear Form Non-Degenerate on a Subspace.

  • caffeinemachine
  • · Replies 5 ·
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5

The equation has exactly m different solutions

  • mathmari
  • · Replies 1 ·
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1

Undergrad Linearly Independent Sets and Spans in R4

  • grassstrip1
  • · Replies 1 ·
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1

Undergrad Can anyone help me fix quaternion rotation errors in Unity?

  • twoski
  • · Replies 15 ·
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15

Graduate Why use the notation (s, a, b, c) for quaternions instead of (s, v)?

  • Septimra
  • · Replies 1 ·
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1

Graduate Understanding the method to solve the cubic equation

  • PcumP_Ravenclaw
  • · Replies 1 ·
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1

Graduate A Large scale eigenvalue problem solver

  • jollage
  • · Replies 5 ·
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5

Split Short Exact Sequences - Bland - Proposition 3.2.6

  • Math Amateur
  • · Replies 2 ·
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2

How Do We Find the Embeddings of $\mathbb{Q}(\sqrt{2})$ in $\mathbb{R}$?

  • mathmari
  • · Replies 1 ·
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1

Proving Intersection of Ideals in $K[x_1,x_2,...,x_n]$

  • evinda
  • · Replies 13 ·
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13
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13

Undergrad Question about row space basis and Column space basis

  • PsychonautQQ
  • · Replies 2 ·
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2

Graduate Adjacency matrices: (a) notation discrepancy, and (b) applications

  • nomadreid
  • · Replies 3 ·
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3

Are the Fields $\mathbb{F}_{2^2}$ and $\mathbb{Z}_2(a)$ Equal?

  • mathmari
  • · Replies 2 ·
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2

Graduate Isomorphism between Clifford algebras CL(4,2) and CL(2,4)

  • mnb96
  • · Replies 4 ·
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4

Categories - Bland Chapter 3 - Problem 2 - Problem Set 3.1

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Can a One-Sided Identity Element in Groups Lead to Two-Sided Identity?

  • HyperActive
  • · Replies 5 ·
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5

Categories - Bland Chapter 3 - Problem 1 - Problem Set 3.1

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Division Algorithm for Polynomials in R[x] confusing me

  • PsychonautQQ
  • · Replies 1 ·
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1

Showcasing $V(I \cap J)=V(I) \cup V(J)$ in Polynomials

  • evinda
  • · Replies 1 ·
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1

Graduate Roots of unity, Roots of complex equations of the form z^n = 1

  • PcumP_Ravenclaw
  • · Replies 2 ·
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2

Undergrad Nonhomogeneous System: Similar Coefficients & Solutions?

  • kosovo dave
  • · Replies 5 ·
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5

Graduate Confusion about position operator in QM

  • ShayanJ
  • · Replies 1 ·
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1

Solving Supply & Demand Equations - Get the Price You Need!

  • GangsterWaffle
  • · Replies 1 ·
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1

Graduate Number of eigenvectors for Hermitian matrices

  • haisydinh
  • · Replies 6 ·
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6

Graduate How do I rotate an inertia tensor in Cartesian coordinates?

  • bugatti79
  • · Replies 4 ·
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4

Undergrad Is the Matrix B Positive or Not?

  • nomadreid
  • · Replies 3 ·
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3

Undergrad Do Matrix Inverses Commute When Flanking Another Matrix?

  • Woolyabyss
  • · Replies 1 ·
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1

Graduate Free Modules: Bland Corollary 2.2.4 - Issue on Finite Generation

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Doubt about rotation isometry on the complex plane

  • PcumP_Ravenclaw
  • · Replies 3 ·
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3

Problem with idempotent matrices

  • Samme013
  • · Replies 5 ·
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5

Commutative rings are IBN-rings - Bland Proposition 2.2.11

  • Math Amateur
  • · Replies 4 ·
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4

Help with Paul E. Bland's Division Rings and IBN-rings Prop 2.2.10 Proof

  • Math Amateur
  • · Replies 1 ·
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1

Free Modules With More Than One Basis - Bland - Example 5, page 56

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Lie Groups, Lie Algebra and Vectorfields

  • JonnyMaddox
  • · Replies 3 ·
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3

Free Modules w/Multiple Bases: 2nd Issue w/Example 5 (Paul E. Bland)

  • Math Amateur
  • · Replies 1 ·
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1

Understanding the Standard Free Right Module on a Set X?

  • Math Amateur
  • · Replies 15 ·
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15

Is $C[x,y,z]/<y-x^2,z-x^3>$ an Integral Domain?

  • evinda
  • · Replies 1 ·
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1

Graduate Solving Cyclic Group Questions: How Many Elements of Order What?

  • jimmycricket
  • · Replies 2 ·
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2

Graduate Our Old Friend, the Twin Primes Conjecture

  • tuttlerice
  • · Replies 11 ·
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11

Endomorphism Rings - Bland Example 7 - page 10

  • Math Amateur
  • · Replies 1 ·
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1

Free Modules - Bland - Proposition 2.2.3

  • Math Amateur
  • · Replies 5 ·
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5

Graduate Is every diagonalizable representation of a group reducible?

  • Faust90
  • · Replies 10 ·
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10

Graduate Proof of the twin primes conjecture

  • StatGuy2000
  • · Replies 3 ·
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3

Free Modules: Solving Issue of Finite Generation Corollary 2.2.4

  • Math Amateur
  • · Replies 3 ·
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3

Free Modules - Another issue regarding Bland Proposition 2.2.4

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Do Row Operations Maintain Equivalence in Matrix Subtraction?

  • MathewsMD
  • · Replies 5 ·
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5

Undergrad Duality and Orthogonality: What's the Difference?

  • janu203
  • · Replies 6 ·
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6

Graduate Projection of a on b when a, b are complex

  • johann1301
  • · Replies 2 ·
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2

Graduate Derivation of rotation isometry on the complex plane

  • PcumP_Ravenclaw
  • · Replies 2 ·
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2

Quadratic form, determine the surface

  • vincentvance
  • · Replies 1 ·
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1

Free Modules - Another problem regarding Bland Proposition 2.2.3

  • Math Amateur
  • · Replies 1 ·
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1

Graduate The adjoint representation of a semisimple Lie algebra is completely reducible

  • maverick280857
  • · Replies 4 ·
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4

Exploring Algebraic Sets: Finding Irreducibility and Prime Ideals

  • evinda
  • · Replies 1 ·
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1

Graduate Some questions about group representations

  • ShayanJ
  • · Replies 7 ·
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7

Proving Maximal Ideal of $\mathbb{C}[X,Y]$

  • evinda
  • · Replies 12 ·
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12

Simple Issue with Submodules - Northcott, Proposition 2, pages 7-8

  • Math Amateur
  • · Replies 2 ·
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2

Sum of an Indexed Family of Submodules - Northcott, pages 8-9

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Is the Direct Product of Two Finite Cyclic Groups Cyclic

  • Bashyboy
  • · Replies 7 ·
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7

Question on rank-nullity theorem

  • SarahER
  • · Replies 2 ·
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2

Undergrad Zero Dimensional Null Space (What's the meaning of this?)

  • kosovo dave
  • · Replies 4 ·
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4

Graduate How do you take a tensor product?

  • space-time
  • · Replies 5 ·
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5

How to solve the following matrix rotation

  • Logan Land
  • · Replies 5 ·
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5

High School Definition of determinant for 2x2 matrix

  • MathewsMD
  • · Replies 2 ·
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2

Finding the Rank and Basis for a matrix

  • Logan Land
  • · Replies 3 ·
Replies
3

SEO) Discovering Matrix 2: A 3x2 Matrix Calculation and Its Applications

  • leprofece
  • · Replies 1 ·
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1

Undergrad Difference between orthogonal transformation and linear transformation

  • EnglsihLearner
  • · Replies 9 ·
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9

Why is the characteristic different from 2?

  • evinda
  • · Replies 2 ·
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2

Undergrad Possible Number of Vertices for Graphs with Three Edge Connections

  • metapuff
  • · Replies 4 ·
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4

Graduate Dihedral Group D_4: Denotations & Correspondence

  • Bashyboy
  • · Replies 3 ·
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3

Undergrad Some help understanding vector space

  • MarcL
  • · Replies 2 ·
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2

Undergrad Need help with some linear algebra questions

  • KevinCT
  • · Replies 1 ·
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1

Finding the Matrix Aij: Cubic Root of 2, -4 Power of j & Sqrt of 3)

  • leprofece
  • · Replies 1 ·
Replies
1

Surjectivity of a Free Module Homomorphism implies injectivity

  • caffeinemachine
  • · Replies 3 ·
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3

Graduate Proof of Left Cosets Partition a Group

  • Bashyboy
  • · Replies 5 ·
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5

Graduate Are the Only Ideals in M(2, R) Trivial?

  • WWGD
  • · Replies 3 ·
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3

External and Internal Direct Sums - Bland - Rings and Their Modules

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Proving vectors are in the column space

  • Taylorw369
  • · Replies 3 ·
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3

Graduate How can Lambert's equation be used to solve for x?

  • psyclone
  • · Replies 2 ·
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2

Undergrad For G = <a: a^100 = e>, find the following

  • CoachBryan
  • · Replies 1 ·
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1

Graduate Solving Computations w/ Cycles: Permutations, Inverses, Orders

  • CoachBryan
  • · Replies 5 ·
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5

Problem about a group with two inner direct product representations

  • stragequark
  • · Replies 3 ·
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3

Elements of the form a/b in an integral domain - simple question

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Proof of Trace Orthogonality Relation for Matrices $\Gamma^A$

  • gentsagree
  • · Replies 1 ·
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1

Find basis and dimension of the intersection of S and T

  • Logan Land
  • · Replies 17 ·
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17

Find the image of a two variable function

  • Synapse0x
  • · Replies 3 ·
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3

Is it true these are theorems in Linear Algebra?

  • Logan Land
  • · Replies 2 ·
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2

Undergrad Algebra experiment using cellophane

  • srfriggen
  • · Replies 4 ·
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4

Graduate Linear Algebra Matrix Transformation to plane

  • FlorenceC
  • · Replies 4 ·
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4

Undergrad Row and Column equivalent matrices

  • PsychonautQQ
  • · Replies 4 ·
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4