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

Linear Applications: Electrical Networks

  • Pull and Twist
  • · Replies 1 ·
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1

Prove Abelian Group: $(a \cdot b)^n = a^n \cdot b^n$

  • Guest2
  • · Replies 1 ·
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1

Two Versions of the Correspondence Theorem for Vector Spaces

  • Math Amateur
  • · Replies 4 ·
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4

Sum of Two Subspaces and lub - Roman, Chapter 1, page 39

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Understanding Equivariant Maps in Group Theory

  • mnb96
  • · Replies 8 ·
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8

Graduate Understanding POVMs and Quantum Information in Corollary Proofs

  • aaaa202
  • · Replies 1 ·
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1

Understand Theorem 2.15 - Bruce Cooperstein's Advanced Linear Algebra

  • Math Amateur
  • · Replies 1 ·
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1

Correspondence Theorem for Vector Spaces - Cooperstein Theorem 2.15

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Calculating Square Root of a Matrix in Quantum Information Theory

  • aaaa202
  • · Replies 10 ·
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10

Can this system of equations be solved analytically?

  • Siron
  • · Replies 3 ·
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3

Undergrad Can an orthogonal matrix be complex?

  • charlies1902
  • · Replies 9 ·
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9

What is the Simplest Form of a Field Extension of the Reals?

  • Kiwi1
  • · Replies 2 ·
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2

Vector Spaces and Linear Transformations - Cooperstein Theorem 2.7

  • Math Amateur
  • · Replies 5 ·
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5

Graduate What are the elements of Lie algebra in the case of a single generator?

  • LagrangeEuler
  • · Replies 11 ·
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11

Is V a Subspace of P2?

  • rayne1
  • · Replies 3 ·
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3

Undergrad Why are linear equations usually written down as matrices?

  • japplepie
  • · Replies 4 ·
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4

Prove F(a,b)=F(a)(b)=F(b)(a) in Field Extensions

  • Scherie
  • · Replies 3 ·
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3

Graduate Factorization of floor functions of fractions

  • DirichletHole
  • · Replies 4 ·
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4

Undergrad Ellipse Rotation: Solving with Normal Rotation Matrix

  • Physgeek64
  • · Replies 12 ·
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12

Roots of an irreducible polynomial over a finite field

  • Scherie
  • · Replies 1 ·
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1

Undergrad Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?

  • Bruno Tolentino
  • · Replies 3 ·
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3

Finding Eigenvalues of Matrix A: Wrong Answer, What Am I Doing Wrong?

  • Yankel
  • · Replies 3 ·
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3

Graduate Local Algebra: intersection multiplicity

  • giulio_hep
  • · Replies 14 ·
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14

Undergrad Why Do Different Definitions of Rotation Matrices Exist in Mathematics?

  • LagrangeEuler
  • · Replies 6 ·
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6

Graduate Where Am I Going Wrong in My Category Theory Solution?

  • nateHI
  • · Replies 6 ·
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6

Vector Spaces - The Exchange Theorem - Cooperstein Theorem 1.16

  • Math Amateur
  • · Replies 7 ·
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7

Undergrad Euler Representation of complex numbers

  • Hijaz Aslam
  • · Replies 6 ·
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6

Graduate Nonlinear coordinate transformation

  • shawnstrausser
  • · Replies 1 ·
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1

Graduate Is My Approach to Matrix Exponentiation Valid?

  • DuckAmuck
  • · Replies 3 ·
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3

High School I have a question about the definition of a vector

  • Chump
  • · Replies 8 ·
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8

Understanding the Constant Field of a Differential Field in $k((x))$

  • mathmari
  • · Replies 1 ·
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1
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3

Matrix Sum of Squares: Rotate Coord System to Express as Diagonal

  • ognik
  • · Replies 9 ·
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9

Short questions relating to field extensions

  • Kiwi1
  • · Replies 9 ·
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9

Undergrad Vector Analysis using Basis Vectors

  • Jimmy87
  • · Replies 5 ·
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5

Basic Exercise in Vector Spaces - Cooperstein Exercise 2, page 14

  • Math Amateur
  • · Replies 5 ·
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5

Basic equation in Vector Space - Cooperstein Exercise 1, Section 1.3

  • Math Amateur
  • · Replies 2 ·
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2

Graduate Tensor Product Functor & Einstein Eqns: Relation?

  • nateHI
  • · Replies 2 ·
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2

Undergrad Proving a set of vectors is linearly independent

  • BillhB
  • · Replies 14 ·
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14

K[T]-Modules and Block Forms of Matrices

  • Math Amateur
  • · Replies 4 ·
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4

Vector Spaces - The Space F^n - Cooperstein Exercise 12, page 10

  • Math Amateur
  • · Replies 1 ·
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1

Undergrad How is the square of a transformed vector not a vector?

  • BHL 20
  • · Replies 7 ·
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7

Quantum Computing: Change of Basis

  • Ackbach
  • · Replies 5 ·
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5

Sums and Intersections of Submodules .... Berrick and Keating Exercise 1.2.12

  • Math Amateur
  • · Replies 1 ·
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1

C[T] modules - Berrick and Keating Exercise 1.2.8 (c)

  • Math Amateur
  • · Replies 4 ·
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4

Polynomials Acting on Spaces - B&K Ex. 1.2.2 (iv): An Intro by Peter

  • Math Amateur
  • · Replies 7 ·
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7

Solver for Value of $a$: Unique, Infinite, No Solution

  • evinda
  • · Replies 4 ·
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4

Solving Systems of Equations with Whole Numbers

  • Yankel
  • · Replies 1 ·
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1

Simple Notational Issue in Roman: "Advanced Linear Algebra"

  • Math Amateur
  • · Replies 2 ·
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2

Undergrad Reduced Echelon Form - Which is correct?

  • L = K - U
  • · Replies 3 ·
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3

Undergrad Eigenvectors and Row/Column Vectors: What's the Connection?

  • Mappe
  • · Replies 3 ·
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3

Graduate Is Every Diagonalizable Endomorphism Defined by a Simple Polynomial?

  • geoffrey159
  • · Replies 12 ·
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12

Graduate Over constrained least squares analysis

  • benzun_1999
  • · Replies 3 ·
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3

Undergrad Can Gauss-Jordan Elimination simplify a matrix into a reduced row echelon form?

  • askor
  • · Replies 16 ·
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16

Is the Matrix Positive Definite?

  • evinda
  • · Replies 6 ·
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6

Finding Unique solution for system of linear equations

  • diggybob
  • · Replies 1 ·
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1

Graduate Group Presentations Isomorphisms

  • MostlyHarmless
  • · Replies 4 ·
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4

Graduate When is the gram matrix positive definite?

  • perplexabot
  • · Replies 2 ·
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2

Graduate A reasonable analogy for understanding similar matrices?

  • kostoglotov
  • · Replies 4 ·
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4

How can we prove that k is an integer?

  • mathmari
  • · Replies 8 ·
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8

Graduate What Are the Subalgebras of Biquaternions?

  • EinsteinKreuz
  • · Replies 2 ·
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2

Prove that there are infinitely many irreducible polynomials in Z5.

  • Kiwi1
  • · Replies 3 ·
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3

Graduate Coriolus effect, precession in 4+1D?

  • Hornbein
  • · Replies 1 ·
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1

Undergrad Simple fundamental subspaces problem stumping me

  • kostoglotov
  • · Replies 3 ·
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3

Undergrad Polar and Jordan Decomp. in Intro to Linear Algebra?

  • kostoglotov
  • · Replies 1 ·
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1

Graduate What is meant by this statement?

  • Amany Gouda
  • · Replies 3 ·
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3

Graduate Tricomplex numbers (Trinions anyone?)

  • EinsteinKreuz
  • · Replies 11 ·
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11

Graduate Constraint on M to keep M^T * A * M positive semidefinite?

  • perplexabot
  • · Replies 2 ·
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2

Insights Matrix Representations of Linear Transformations - Comments

  • Fredrik
  • · Replies 19 ·
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19

Graduate Example of an algebra tensor product

  • Geofleur
  • · Replies 17 ·
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17

Graduate The equivalence of a set and its permutations.

  • Odious Suspect
  • · Replies 3 ·
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3

Undergrad Transpose: a linear transformation?

  • kostoglotov
  • · Replies 2 ·
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2

Interpreting & Solving Nullspace

  • cbarker1
  • · Replies 2 ·
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2

Proof that the solutions are algebraic functions

  • mathmari
  • · Replies 1 ·
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1

Graduate Difference between R^{4} and R^{1,3}

  • spaghetti3451
  • · Replies 1 ·
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1

Graduate What Are the Fascinating Rotations of 3-Spheres in 4D Space?

  • Hornbein
  • · Replies 13 ·
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13

Graduate What is the meaning of the term "dual"?

  • "Don't panic!"
  • · Replies 15 ·
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15

Graduate Why do we care about spin groups?

  • Apogee
  • · Replies 1 ·
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1

Why Are Eigenvalues and Eigenvectors Important in Linear Algebra?

  • Yankel
  • · Replies 3 ·
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3

Graduate Am I verifying that this is a group correctly?

  • gavin123
  • · Replies 7 ·
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7

Undergrad Understanding the Role of Matrix Multiplication in Solving Equations

  • Martin V.
  • · Replies 2 ·
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2

Graduate Is My SDP Formulation to Minimize trace((G^TG)^-1) Correct?

  • perplexabot
  • · Replies 1 ·
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1

Graduate Verifying the Fourier Series is in Hilbert Space

  • kostoglotov
  • · Replies 2 ·
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2
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17

Graduate Lie group multiplication and Lie algebra commutation

  • spaghetti3451
  • · Replies 5 ·
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5

Graduate Graphing Eigenvectors and Sine Curves: Understanding the Relationship

  • kostoglotov
  • · Replies 9 ·
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9

Graduate Backwards difference matrix divided by negative delta x?

  • kostoglotov
  • · Replies 3 ·
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3

Graduate Tensor in D-dimensional space crosswise with 2 vectors

  • olgerm
  • · Replies 3 ·
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3

What is the Dot Product of u+v?

  • karush
  • · Replies 3 ·
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3

Graduate Example of a factor space in physics

  • Geofleur
  • · Replies 10 ·
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10

Undergrad Simple showing inverse of matrix also upper triangular

  • snrwww
  • · Replies 6 ·
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6
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3

Graduate Deriving the structure constants of the SO(n) group

  • spaghetti3451
  • · Replies 9 ·
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9
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5

Graduate Deriving the commutation relations of the so(n) Lie algebra

  • spaghetti3451
  • · Replies 7 ·
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7
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5

How Do You Calculate the Determinant of a Matrix Using Index Notation?

  • ognik
  • · Replies 2 ·
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2
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8

Graduate Can Matrix Determinants Be Used to Find Optimal Area in Higher Dimensions?

  • vin300
  • · Replies 2 ·
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2

Uniqueness of Inverse Matrices: Proof and Explanation

  • ognik
  • · Replies 13 ·
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13