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 M-<M> for M operator: why not a mismatch?

  • nomadreid
  • · Replies 2 ·
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2

Matrix multiplication simplified to Vector multiplication

  • CyanBC
  • · Replies 2 ·
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2

Eigenvalues of Laplacian are non-negative

  • tarnat
  • · Replies 1 ·
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1

Ring Theory texts and "right notation" for maps/functions

  • Math Amateur
  • · Replies 6 ·
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6

Is There a Typo in the Refinement of Schanuel's Lemma in Passman's Book?

  • Sudharaka
  • · Replies 4 ·
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4

Finitely Generated Modules and Artinian Rings

  • Sudharaka
  • · Replies 6 ·
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6
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16

Is a Prime Artinian Ring Simple?

  • Sudharaka
  • · Replies 1 ·
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1

Ring Epimorphism and Nil Radical

  • Sudharaka
  • · Replies 5 ·
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5

How Do Scalars Relate to Unit Vectors Inclined at Angle Theta?

  • Saitama
  • · Replies 13 ·
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13

What are some recommended texts for studying algebraic topology?

  • Math Amateur
  • · Replies 3 ·
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3

New to Linear Algebra - LU Decomposition

  • pp123123
  • · Replies 2 ·
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2

Exact Sequences - D&F Section 10.5, Proposition 27

  • Math Amateur
  • · Replies 3 ·
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3

Exterior powers of a vector space and its dual space

  • Jakob1
  • · Replies 2 ·
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2

Graduate Higher dimensional cross products

  • zephyr5050
  • · Replies 3 ·
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3

Help solving a linear equation in one variable

  • kmooney
  • · Replies 19 ·
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19

Graduate Finding satisfying matrix for a particular condition

  • Seydlitz
  • · Replies 2 ·
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2

How Can Group Homomorphisms Prove Injectivity and Surjectivity?

  • Math Amateur
  • · Replies 10 ·
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10

Graduate Fourier transform vs Inner product

  • Bipolarity
  • · Replies 3 ·
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3

How to Calculate the Area Between Two Vectors in R^n?

  • poissonspot
  • · Replies 1 ·
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1

Invariant subspaces of representations

  • Carla1985
  • · Replies 9 ·
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9

Graduate LTI system and sinusoids/complex exponentials

  • Bipolarity
  • · Replies 7 ·
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7

Category Theory - Isomorphisms of Posets

  • Math Amateur
  • · Replies 6 ·
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6

Solving for X in Matrix Equation: C^TA-XB=B^{-1}-X

  • theakdad
  • · Replies 2 ·
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2

Category Theory - is it just "abstract nonsense"

  • Math Amateur
  • · Replies 12 ·
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12

Graduate Product of the conjugates of a polynomial

  • coquelicot
  • · Replies 1 ·
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1

Proving the Planarity of a Quadrilateral using Vector Algebra

  • Saitama
  • · Replies 4 ·
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4

Graduate Free groups: why are they significant in group theory?

  • James MC
  • · Replies 7 ·
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7

Graduate What Are the Key Properties and Questions About Free Modules?

  • gianeshwar
  • · Replies 2 ·
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2

Exact Sequences - Split Sequences and Splitting Homomorphisms

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Is the Jacobian Equal to the Quotient of Scale Factors?

  • Jhenrique
  • · Replies 1 ·
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1

Undergrad Unit vector in cylindrical coordinates

  • JasonHathaway
  • · Replies 1 ·
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1

Graduate Modifying a transformation based on yaw-pitch-roll or phi-theta-psi

  • amrbekhit
  • · Replies 2 ·
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2

Graduate Solving nonlinear equations for yaw/pitch/roll given rotor/quaternio

  • chogg
  • · Replies 1 ·
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1

Undergrad Is 1D Space a Subspace of 2D Space in Physics?

  • gianeshwar
  • · Replies 4 ·
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4

Exact Sequences - Isomorphisms Resulting from Exact Sequences

  • Math Amateur
  • · Replies 3 ·
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3

Graduate (empirical) relation between MSE and condition number

  • divB
  • · Replies 1 ·
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1

Each equivalence class is a power of [g]

  • evinda
  • · Replies 3 ·
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3

Graduate Shilov's Linear Algebra Subspace Question

  • Chacabucogod
  • · Replies 11 ·
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11

State Matrix Derivation for Orbital Mechanics

  • Dustinsfl
  • · Replies 1 ·
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1

Graduate Exploring the Generalization of Mercer's Theorem to Square Integrable Functions

  • mnb96
  • · Replies 1 ·
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1

Tensor Products - Example 8 - Dummit and Foote - Section 10.4, page 370

  • Math Amateur
  • · Replies 5 ·
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5

Understanding D&F Example 2: R/I Bimodule on Page 366

  • Math Amateur
  • · Replies 1 ·
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1

Graduate Ideal representation for vectors/covectors

  • Jhenrique
  • · Replies 2 ·
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2

Graduate What are reliable references for the theorem on integral extensions?

  • coquelicot
  • · Replies 9 ·
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9

Vector Algebra: Finding the Angle Between Two Vectors

  • Saitama
  • · Replies 6 ·
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6

Simple Problem - Establishing an Isomorphism

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Free columns-combinations of columns?

  • sarvesh0303
  • · Replies 2 ·
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2

Factor a^4+b^4: Simplify \(a^4 + b^4 \)

  • Dustinsfl
  • · Replies 6 ·
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6

Tensor Products - D&F page 369 Example 2

  • Math Amateur
  • · Replies 16 ·
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16

Graduate Why Does Matrix B & C Result in Matrix A?

  • SmilingDave
  • · Replies 9 ·
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9

Undergrad A question about the cross product as related to matrix multiplication

  • RufusDawes
  • · Replies 9 ·
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9

Tensor Products - D&F page 369 Example 3 - The map phi

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Finding a Transformation Matrix for Matching Signs in a Matrix

  • Phong
  • · Replies 1 ·
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1

Simple Problem concerning tensor products

  • Math Amateur
  • · Replies 1 ·
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1

High School Differences between row and column vectors

  • Quarlep
  • · Replies 25 ·
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25

Undergrad Finding Angle Between Two Vectors Using Inner Products

  • Cameron95
  • · Replies 7 ·
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7

Graduate Proving the Falsehood of the Homomorphism Property for Ω:Zp^n→Zp^n

  • Bachelier
  • · Replies 5 ·
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5

Undergrad Struggling with Linear Algebra: Where to Find Help?

  • mathsdespair
  • · Replies 5 ·
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5

Graduate How Did the Definition of a Field Evolve to Require Commutativity?

  • Stephen Tashi
  • · Replies 1 ·
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1

Some help on a matrix question please.

  • khehrap
  • · Replies 4 ·
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4

Graduate What is the difference between unit vectors v and r?

  • Jhenrique
  • · Replies 1 ·
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1

Graduate Why this property of the product of two matrices

  • senmeis
  • · Replies 5 ·
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5

Tensor Products - Dummit and Foote Section 10.4, Example 2, page 363

  • Math Amateur
  • · Replies 4 ·
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4

Tensor Products - Dummit and Foote Section 10.4 Corollary 9

  • Math Amateur
  • · Replies 37 ·
2
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37

High School Can We Subtract Matrices with Different Dimensions?

  • Quarlep
  • · Replies 1 ·
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1

How do you find frobenius canonical form of a matrix?

  • catsarebad
  • · Replies 1 ·
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1

Undergrad Theory for find the eigenvules of a matrix

  • Jhenrique
  • · Replies 4 ·
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4

Proving Linear Dependence of r1,r2,r3 Given a,b,c ≠ 0

  • Suvadip
  • · Replies 2 ·
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2

Solve Linear Equations: 1/5(1/3x-5)=1/3(3-1/x)

  • abhishekdas1
  • · Replies 7 ·
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7

Two sets generate the same vector space

  • Suvadip
  • · Replies 1 ·
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1

Graduate If A, B Hermitian, then <v|AB|v>=<v|BA|v>*. Why?

  • nomadreid
  • · Replies 2 ·
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2

Undergrad Guidance: Convex hull, null space and convex basis etc

  • Inner_Peace
  • · Replies 3 ·
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3

Could someone recommend me pure math linear algebra book?

  • catsarebad
  • · Replies 12 ·
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12

Graduate Is every norm preserved under a unitary map?

  • Bipolarity
  • · Replies 2 ·
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2

How to Prove Certain Matrix Operations and Understand Their Properties?

  • akerman
  • · Replies 13 ·
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13

Greatest common divisor of a and b

  • mathmari
  • · Replies 8 ·
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8

Is There Only One Possible Z-Linear Map from T to T'?

  • Math Amateur
  • · Replies 18 ·
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18

Graduate Hilbert, Banach and Fourier theory

  • center o bass
  • · Replies 3 ·
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3

What is vector in linear algebra

  • Suvadip
  • · Replies 17 ·
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17

Show all invariant subspaces are of the form

  • catsarebad
  • · Replies 2 ·
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2

Graduate Centerless Groups: Examples & Constraints

  • gentsagree
  • · Replies 3 ·
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3

Tensor Products - The free Z-module construction

  • Math Amateur
  • · Replies 10 ·
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10

Graduate Does there exist a canonical projection from Z^p-1 to Z_p

  • NoodleDurh
  • · Replies 3 ·
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3

Tensor Products - D&F - Extension of the scalars

  • Math Amateur
  • · Replies 2 ·
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2

History of Algebra: Modern Algebra, Ring Theory, Algebraic Topology

  • Math Amateur
  • · Replies 6 ·
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6

Undergrad Why do we learn Dual Space so early?

  • Vorde
  • · Replies 4 ·
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4

Undergrad Calculating Solid Angle Between Three Vectors: A Scientific Guide

  • Jhenrique
  • · Replies 2 ·
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2

Tensor Products - Dummit and Foote - Section 10-4, Theorem 8, page 362

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Row selection of matrix and the condition number

  • divB
  • · Replies 10 ·
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10

Graduate Lie theory - sum of nilpotent ideals is nilpotent?

  • Silversonic
  • · Replies 2 ·
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2

Undergrad Can a Linear Transformation Satisfy One Property but Not the Other?

  • Gridvvk
  • · Replies 4 ·
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4

Matrix Exponential and series idenfication

  • Dustinsfl
  • · Replies 6 ·
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6

Understanding How to Solve Vector Magnitudes and Angles

  • bergausstein
  • · Replies 1 ·
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1

System of Equations II: Evaluate p+q+r+s & 64p+27q+8r+s

  • anemone
  • · Replies 7 ·
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7

Undergrad Having trouble understanding minimal polynomial problems

  • catsarebad
  • · Replies 4 ·
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4

Undergrad A deeper understanding of the determinate

  • TackyJan
  • · Replies 8 ·
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8

Undergrad Simple Proofs for Matrix Algebra Properties: A Beginner's Guide

  • leehufford
  • · Replies 3 ·
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3

Construct a matrix with such that V is not equal to C_x

  • catsarebad
  • · Replies 5 ·
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5

Undergrad How Do Unit Vectors Achieve Their Form?

  • JasonHathaway
  • · Replies 9 ·
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9