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

Undergrad Vector notation - form versus vector?

  • MrNeu
  • · Replies 9 ·
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9

Help understanding proof for Capon Method

  • Milliarde
  • · Replies 6 ·
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6

Graduate Is There a Linear Transformation to Map Data Set X to Y in PCA?

  • Trentkg
  • · Replies 4 ·
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4

Undergrad How Do I Understand <g> in Z/mZ?

  • Convergence
  • · Replies 1 ·
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1

Field Theory - Element u transcendental of F

  • Math Amateur
  • · Replies 3 ·
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3

Graduate What is the Connection Between Matrix Trace and Endomorphism?

  • tamintl
  • · Replies 1 ·
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1

Graduate Is absorption an axiom for a boolean algebra?

  • Bipolarity
  • · Replies 3 ·
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3

Determine the matrices that represent the following rotations of R^3

  • kalish1
  • · Replies 2 ·
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2

Graduate Finding the elements of a group given two generators and relations

  • Dixanadu
  • · Replies 26 ·
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26

A proof of a general property of norms

  • gucci1
  • · Replies 1 ·
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1

Graduate Proof of a linear operator acting on an inverse of a group element

  • Dixanadu
  • · Replies 4 ·
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4

High School Help taking a cross product of a matrix

  • member 428835
  • · Replies 3 ·
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3

Prove A=B when A⊂span(B) and B⊂span(A)

  • toni07
  • · Replies 2 ·
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2

Splitting Fields - Dummit and Foote - Example - page 541 - x^p - 2, p prime

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Understanding Mathematical Structures

  • Jimmy84
  • · Replies 1 ·
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1

Undergrad Linear independance best methods?

  • tamintl
  • · Replies 11 ·
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11

Graduate Can a 2N by 2N matrix written in terms of N by N matrices?

  • sokrates
  • · Replies 3 ·
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3
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6

Redundancy in Question about Linear Transformations

  • Sudharaka
  • · Replies 3 ·
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3

Matrix L1-Norm: Max of Column Sums Explained

  • gucci1
  • · Replies 1 ·
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1

The Meaning of Degenerate in the Context of Linear Algebra

  • Sudharaka
  • · Replies 2 ·
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2

Find a Basis for Subspace in P_3(\mathbb{R})

  • Petrus
  • · Replies 11 ·
Replies
11

Understanding Matrix Units for Linear Transformations in M2(Re)

  • Sudharaka
  • · Replies 10 ·
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10

Undergrad Would The Cross Product of x and x be z0?

  • Meadman23
  • · Replies 4 ·
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4

Solving Linear Transformations w/ Bases of Vector Spaces

  • Chris L T521
  • · Replies 4 ·
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4

Can $S_5$ be written as a multiple of $S_3$ and $S_2$?

  • anemone
  • · Replies 2 ·
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2

Splitting Fields - Dummit and Foote - Exercise 1, page 545

  • Math Amateur
  • · Replies 3 ·
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3

Find the eigenvalue of a linear map

  • Barioth
  • · Replies 2 ·
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2

Undergrad Using linear algebra to find a number of independent equations

  • member 392791
  • · Replies 5 ·
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5

Field Theory - Basic Theory - D&F Section 13.1

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Does a Linear Combination of Vectors in an Infinite Set Have to Be Finite?

  • Bipolarity
  • · Replies 3 ·
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3

Graduate Solving Density Problems in Number Theory

  • DeadOriginal
  • · Replies 10 ·
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10

Determinant Property: Seen it Before? True?

  • Dustinsfl
  • · Replies 2 ·
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2

Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 2, page 529

  • Math Amateur
  • · Replies 4 ·
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4

Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 4, page 530

  • Math Amateur
  • · Replies 3 ·
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3

Graduate Some subset of a generating set is a basis

  • Bipolarity
  • · Replies 11 ·
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11

Undergrad Where Can I Find Linear Algebra Practice Problems for First Year Undergraduates?

  • matqkks
  • · Replies 6 ·
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6

Solving $x$ in Terms of $a$: $x^4-3ax^3+3a^3x+a^4=0$

  • anemone
  • · Replies 7 ·
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7

Graduate Is Every Finite Dimensional Lie Algebra Isomorphic to a Subalgebra of GL(n)?

  • Kontilera
  • · Replies 1 ·
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1

Graduate If f and g are orthogonal, are f* and g orthogonal?

  • Aziza
  • · Replies 2 ·
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2

Undergrad Cross product to find the area of a triangle

  • molly1103
  • · Replies 1 ·
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1

Undergrad Need help understanding Superposition Principle

  • shivaniits
  • · Replies 4 ·
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4

Undergrad What is the cross product of 5k and 3i+4j?

  • B4ssHunter
  • · Replies 3 ·
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3

Can someone solve this System, (1equation, 3 variables)

  • ends
  • · Replies 1 ·
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1

Algebraic Extensions: Dummit & Foote Section 13.2, Example 2 pg 526 - Help!

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Linearity of boolean expressions

  • m~ray
  • · Replies 5 ·
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5

Field Theory - Algebrais Extensions - Dummit and Foote Section 13.2

  • Math Amateur
  • · Replies 4 ·
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4

Graduate If AB is invertible, then A and B are invertible.

  • Bipolarity
  • · Replies 14 ·
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14

Undergrad Squaring of vectors in absolute value

  • M. next
  • · Replies 5 ·
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5

Field Extensions - Dummit and Foote Chapter 13 - Exercise 2, page 519

  • Math Amateur
  • · Replies 1 ·
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1

Confused About Exercise 11 Answer Key

  • Petrus
  • · Replies 9 ·
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9

Undergrad What formula or principle governs this observed phenomena?

  • VMey
  • · Replies 2 ·
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2

Spanning set of vectors question

  • gucci1
  • · Replies 2 ·
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2
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1

Graduate Can a point view another point around an obstructing point?

  • wiyosaya
  • · Replies 4 ·
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4

Proof of a linear transformation not being onto

  • baseball3030
  • · Replies 6 ·
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6

Proving Linear Maps are One-to-One

  • baseball3030
  • · Replies 2 ·
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2

Field Theory - Dummit and Foote Ch 13 - Exercise 1, page 519

  • Math Amateur
  • · Replies 11 ·
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11

Solving a system of linear equations with one unknown value

  • sparrow1
  • · Replies 1 ·
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1

4x4 Matrix with rank B=4 and B^2=3

  • Petrus
  • · Replies 7 ·
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7

Field Extensions, Polynomial Rings and Eisenstein's Criterion

  • Math Amateur
  • · Replies 1 ·
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1

How Do D&F Derive \(a(x)(1 + x) + b(x)(x^3 - 2) = 1\)?

  • Math Amateur
  • · Replies 2 ·
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2

A linear transformation is invertible if and only if

  • baseball3030
  • · Replies 9 ·
Replies
9

Finding the Unknowns: Solving a 4x4 Linear System of Equations

  • anemone
  • · Replies 6 ·
Replies
6

Graduate How Do Quaternions Enhance Understanding of 3D Rotations?

  • Septimra
  • · Replies 14 ·
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14

Graduate Algebraic properites of the direct sum

  • Bipolarity
  • · Replies 4 ·
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4

Undergrad 2 Rotations on different coordinate systems

  • mostarac2487
  • · Replies 7 ·
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7

Can You Find a Matrix with Ranking Requirements?

  • Petrus
  • · Replies 8 ·
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8

What is the expression for |c_n| in terms of the given matrice?

  • Petrus
  • · Replies 11 ·
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11

Undergrad Why Is the Dimension of the Solution Space n-r in Linear Algebra?

  • ajayguhan
  • · Replies 5 ·
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5

Undergrad Linear transformation from [-1,1] to [a,b]

  • mercuryman
  • · Replies 1 ·
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1

Graduate Solvable group: decomposable in prime order groups?

  • nonequilibrium
  • · Replies 2 ·
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2

Problem involving matrix multiplication and dot product in one proof

  • gucci1
  • · Replies 6 ·
Replies
6

Undergrad Equivalent statements to matrix A is orthogonal

  • CAVision
  • · Replies 1 ·
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1

Undergrad Should You Study All Proofs in Gallian's Abstract Algebra?

  • kvkenyon
  • · Replies 1 ·
Replies
1

Graduate Eigenstate to eigenstate evolution with no intermediate superposition?

  • James MC
  • · Replies 6 ·
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6

Undergrad Linear Transformation: Does T(V) ⊆ W?

  • DeadOriginal
  • · Replies 6 ·
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6

Graduate Non-linear multivariable functions

  • m~ray
  • · Replies 1 ·
Replies
1

Graduate Looking for a proof regarding Baker-Campell-Hausdorff

  • Kontilera
  • · Replies 1 ·
Replies
1

Algebraic Geometry Basics for Understanding Tensegrity in Masters Thesis

  • caffeinemachine
  • · Replies 7 ·
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7

Tensor notation for vector product proofs

  • skate_nerd
  • · Replies 11 ·
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11

Undergrad Is the Triple Scalar Product Always Zero?

  • member 392791
  • · Replies 2 ·
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2

If c|ab and gcd(b, c) = 1 why does c|ac?

  • MI5
  • · Replies 4 ·
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4

Graduate Roots and root vectors of sp(4,\mathbb{R})

  • MathematicalPhysicist
  • · Replies 4 ·
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4

Undergrad What Are the Benefits of Using Discrete Cosine Transform?

  • DUET
  • · Replies 1 ·
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1

Undergrad Closure in Groups: Definition & Examples

  • bonfire09
  • · Replies 4 ·
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4

Undergrad What Does Zero Empirical Mean in Data Matrices?

  • DUET
  • · Replies 1 ·
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1

Undergrad How Does the Covariance Matrix Apply to Vectors X and Y?

  • DUET
  • · Replies 7 ·
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7

Undergrad Understanding Algebra: Step-by-Step Guide from vout to vcm and vd

  • simpComp
  • · Replies 10 ·
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10

Graduate Proving the scalar matrices are the center of the matrix ring

  • Bipolarity
  • · Replies 1 ·
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1

Undergrad The sample covariance of N observations of K

  • DUET
  • · Replies 6 ·
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6

Graduate Extending the basis of a T-invariant subspace

  • Bipolarity
  • · Replies 1 ·
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1

Graduate Question on conjugation closure of subgroups

  • mnb96
  • · Replies 4 ·
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4

What are the properties of orthogonal matrices?

  • Jameson
  • · Replies 15 ·
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15

Graduate Direct sum of nullspace and range

  • Bipolarity
  • · Replies 3 ·
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3

Tricky Linear Algebra Question. To show that an operator is 'cyclic'.

  • caffeinemachine
  • · Replies 6 ·
Replies
6

Solving Householder Matrix Problem

  • Jameson
  • · Replies 2 ·
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2

Construct Orthogonal Basis in R^3: Solve Exercise

  • evinda
  • · Replies 14 ·
Replies
14

Graduate Question about isomorphic mapping on direct sums?

  • Ishida52134
  • · Replies 1 ·
Replies
1

Field Theory - Dummit and Foote - Chapter 13 - Theorem 6

  • Math Amateur
  • · Replies 2 ·
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2