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 Matrix Rings - Basic Problem with Meaning of Notation

  • Math Amateur
  • · Replies 8 ·
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8

How Do You Interpret Rowen's Notation in Matrix Rings?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad How Do Elementary Operations Affect Matrix Rank Preservation?

  • swampwiz
  • · Replies 4 ·
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4

High School Matrix A^(m+1) is different from A^(1+m)?

  • Aldnoahz
  • · Replies 2 ·
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2

Undergrad Existence of basis for P_2 with no polynomial of degree 1

  • Mr Davis 97
  • · Replies 13 ·
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13

Proof that M is Noetherian if N and M/N are Noetherian

  • Math Amateur
  • · Replies 4 ·
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4

Graduate Algebra - Clifford, Dirac, Lorentz

  • spaghetti3451
  • · Replies 1 ·
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1

Graduate How Do Ladder Operators Annihilate States in SU(2) Algebra?

  • spaghetti3451
  • · Replies 6 ·
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6

Is this a valid proof for the invertibility of $\Phi$?

  • rputra
  • · Replies 5 ·
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5

Undergrad Proof that every basis has the same cardinality

  • member 587159
  • · Replies 2 ·
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2

Undergrad Nonempty Subspace: Proving 0u = 0

  • Mr Davis 97
  • · Replies 2 ·
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2

Show That $F(S)$ Is the Smallest Subfield of $K$

  • mathmari
  • · Replies 4 ·
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4

Show that Q[π] is not a subset of Q(π)

  • mathmari
  • · Replies 8 ·
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8

Undergrad Questions about linear transformations

  • Mayan Fung
  • · Replies 10 ·
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10

Undergrad Understanding rectangular matrices

  • Urmi Roy
  • · Replies 7 ·
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7

Finding the Matrix Associated with a Linear Mapping on a Real Matrix

  • rputra
  • · Replies 9 ·
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9

Graduate Question on Cauchy-Schwarz inequality

  • mnb96
  • · Replies 8 ·
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8

Find Group $G$ with Infinite Order Element: Ablien Not Allowed

  • alexmahone
  • · Replies 8 ·
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8

Proving Divisibility of Polynomials in Field Extensions

  • mathmari
  • · Replies 2 ·
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2

Undergrad Lemma 1.2.21 on maximal submodules in Berrick and Keating

  • Math Amateur
  • · Replies 5 ·
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5

Undergrad Existence of minimal generating sets in Berrick and Keating Lemma 1.2.21

  • Math Amateur
  • · Replies 13 ·
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13

Undergrad Is v(r) equivalent to v(x,y,z)?

  • xoxomae
  • · Replies 1 ·
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1

Determinant of matrix with Aij = min(i, j)

  • nedf
  • · Replies 3 ·
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3

Lemma 1.2.21 in Berrick and Keating: minimal generating sets

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Components of functions in vector spaces

  • DoobleD
  • · Replies 10 ·
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10

Graduate For finite dimension vector spaces, all norms are equivalent

  • ShayanJ
  • · Replies 7 ·
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7

High School Why can't I divide both sides by (B² + I) in matrix algebra?

  • Clara Chung
  • · Replies 1 ·
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1

I=<f> is maximal iff f is irreducible

  • mathmari
  • · Replies 12 ·
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12

Proving Convex Set Properties to Showing the Convexity of X-Y

  • rputra
  • · Replies 3 ·
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3

Undergrad I don't quite understand what i read

  • Terrell
  • · Replies 8 ·
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8
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2

How can the convexity of a disk be proved using linear algebra?

  • rputra
  • · Replies 4 ·
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4

Undergrad Finitely Generated Ideals and Noetherian Rings

  • Math Amateur
  • · Replies 7 ·
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7

Finite Extension Simple iff Purely Inseparable Closure Simple

  • caffeinemachine
  • · Replies 1 ·
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1

Show That F[u]=F(u): Proving with Theorem

  • mathmari
  • · Replies 2 ·
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2
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2

Undergrad Left ideal property of direct sum in triangular matrix rings

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad How Do You Prove a Matrix Ring is Right Artinian But Not Left Artinian?

  • Math Amateur
  • · Replies 8 ·
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8

Undergrad Bijection between cosets and subgroup in Lagrange's theorem

  • TeethWhitener
  • · Replies 2 ·
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2

Undergrad Linear least-squares method and row multiplication of matrix

  • Mesud1
  • · Replies 2 ·
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2

Proving disjoint of Kernel and Image of a linear mapping

  • rputra
  • · Replies 2 ·
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2

How Do You Prove a Mapping is Surjective?

  • rputra
  • · Replies 3 ·
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3

Left ideal property of direct sum in triangular matrix rings

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad Showing quotient isomorphisms for triangular matrix rings

  • Math Amateur
  • · Replies 3 ·
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3

Proving isomorphisms for quotients of triangular matrix rings

  • Math Amateur
  • · Replies 1 ·
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1

Is G an Abelian Group Given Specific Conditions?

  • alexmahone
  • · Replies 5 ·
Replies
5

Undergrad Why do eigenvectors stay the same when a matrix is squared?

  • Aldnoahz
  • · Replies 4 ·
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4

Undergrad Concrete Examples of Exact Sequences in Linear Algebra

  • andrew s 1905
  • · Replies 13 ·
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13

What are the ideals of the matrix ring?

  • Math Amateur
  • · Replies 6 ·
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6

Exercise 5.1 (ii) from Rotman's Advanced Modern Algebra on maximal ideals

  • Math Amateur
  • · Replies 6 ·
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6

Example on Triangular Rings - Lam, Example 1.14

  • Math Amateur
  • · Replies 4 ·
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4

Undergrad Why does mr = 0 in Lam's triangular ring example?

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Points of a finite projective line

  • Lapidus
  • · Replies 1 ·
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1

Approaching Question C1: Finding Roots of Elements in a Field

  • Kiwi1
  • · Replies 4 ·
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4

High School How do we know if something is vector or scalar quantity?

  • Faiq
  • · Replies 6 ·
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6

Undergrad Expanding linear independent vectors

  • member 428835
  • · Replies 2 ·
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2

Undergrad Are discontinuous functions closed under addition?

  • member 428835
  • · Replies 3 ·
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3

Undergrad How to Construct an Orthonormal Basis for a 2D Subspace in Linear Algebra?

  • vibe3
  • · Replies 3 ·
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3

Graduate Expectation operation for covariance calculation

  • nikozm
  • · Replies 1 ·
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1

Undergrad Coordinate transformation of a vector of magnitude zero

  • Battlemage!
  • · Replies 3 ·
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3

Undergrad Fundamental Theorem of Arithmetic - Bhattacharya et al

  • Math Amateur
  • · Replies 5 ·
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5

Fundamental Theorem of Arithmetic - Bhattacharya et al - Ch. 2, Section 1

  • Math Amateur
  • · Replies 4 ·
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4

Exercise 5.1(iii) from Rotman's Advanced Modern Algebra

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Are the columns space and row space same for idempotent matrix?

  • arpon
  • · Replies 6 ·
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6

A little problem on exact sequences, part 2.

  • steenis
  • · Replies 4 ·
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4

Why does a|p imply associates or unit in Theorem 5.12?

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Newton's formula for the sums of powers of roots?

  • Clara Chung
  • · Replies 2 ·
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2

Prove Z7 is a Ring Under + and x Operations

  • Zoey93
  • · Replies 3 ·
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3

Undergrad Why does a|p in a PID imply a and p are associates or a is a unit?

  • Math Amateur
  • · Replies 4 ·
Replies
4

How Does the Correspondence Theorem for Rings Prove Maximal Ideals?

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Maximal Ideals and the Correspondence Theorem for Rings

  • Math Amateur
  • · Replies 3 ·
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3

Normal Extensions and Normal Subgroups

  • Kiwi1
  • · Replies 1 ·
Replies
1

A little problem on exact sequences.

  • steenis
  • · Replies 7 ·
Replies
7

Undergrad Constructing a vector from a point

  • Mr Davis 97
  • · Replies 2 ·
Replies
2

Undergrad Transpose Property (where's my mistake)

  • member 428835
  • · Replies 3 ·
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3

Undergrad A double in this example problem

  • Muthumanimaran
  • · Replies 3 ·
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3

Undergrad Show that the diagonals are perpendicular using vectors

  • Mr Davis 97
  • · Replies 2 ·
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2

High School Vector perpendicular to a plane defined by two vectors

  • Mr Davis 97
  • · Replies 5 ·
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5

Vector in 3d with given by magnitude and angle

  • cbarker1
  • · Replies 1 ·
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1

Undergrad Use Lorentz Force to Find Magnetic Field Components

  • peasqueeze
  • · Replies 6 ·
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6

Undergrad Can RREF be used for any size matrix?

  • Mr Davis 97
  • · Replies 9 ·
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9

Undergrad Matrix Component Equation: Solving for B with Known Scalar and Indices

  • member 428835
  • · Replies 4 ·
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4

Undergrad Kronecker Delta summation (easy)

  • member 428835
  • · Replies 6 ·
Replies
6

High School The equation relating a vector to a unit vector

  • Mr Davis 97
  • · Replies 6 ·
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6

Prove: \(F(a,b)^*=F(a) \cup F(b)\)

  • Kiwi1
  • · Replies 4 ·
Replies
4

Finding the cheaper store using matrix multiplication

  • mathlearn
  • · Replies 5 ·
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5

Undergrad Why {ras} isn't closed under addition in noncommutative rings

  • Math Amateur
  • · Replies 3 ·
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3

Why {ras | r, s ∈ R} lacks closure under addition in noncommutative rings

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Understanding SU(2) Representations and Their Role in Particle Physics

  • Silviu
  • · Replies 2 ·
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2

Undergrad Module Over a Division Ring - Blyth Theorem 1.1, Part 4

  • Math Amateur
  • · Replies 11 ·
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11

Undergrad State of a Generator in Representation Theory

  • Silviu
  • · Replies 3 ·
Replies
3

High School Tensor Calculus vs Tensor Analysis?

  • ibkev
  • · Replies 2 ·
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2

Undergrad What is the name of the matrix decomposition with specific properties?

  • Ken Gallock
  • · Replies 6 ·
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6

Undergrad No problem, it's always good to have multiple sources!

  • Silviu
  • · Replies 6 ·
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6

Finding the zero vector of a sinusoidal set

  • Apricity
  • · Replies 2 ·
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2

Why A + B is smallest and A ∩ B is largest submodule

  • Math Amateur
  • · Replies 3 ·
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3

Undergrad Proving A + B is smallest and A ∩ B is largest submodule

  • Math Amateur
  • · Replies 2 ·
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2

Theorem 2.3: Submodule Generation by Family of Submodules - T. S. Blyth

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Finite sums from submodule union in Blyth's Theorem 2.3

  • Math Amateur
  • · Replies 2 ·
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2

High School Is the Inverse of this Matrix Possible?

  • askor
  • · Replies 12 ·
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12