Linear and Abstract Algebra Forum

Post thread
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.
MHB Roots of an irreducible polynomial over a finite field
  • · Replies 1 ·
Replies
1
Views
2K
Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Finding Eigenvalues of Matrix A: Wrong Answer, What Am I Doing Wrong?
  • · Replies 3 ·
Replies
3
Views
2K
Local Algebra: intersection multiplicity
  • · Replies 14 ·
Replies
14
Views
3K
Why Do Different Definitions of Rotation Matrices Exist in Mathematics?
  • · Replies 6 ·
Replies
6
Views
2K
Where Am I Going Wrong in My Category Theory Solution?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Vector Spaces - The Exchange Theorem - Cooperstein Theorem 1.16
  • · Replies 7 ·
Replies
7
Views
2K
Euler Representation of complex numbers
  • · Replies 6 ·
Replies
6
Views
2K
Nonlinear coordinate transformation
  • · Replies 1 ·
Replies
1
Views
2K
Is My Approach to Matrix Exponentiation Valid?
  • · Replies 3 ·
Replies
3
Views
2K
I have a question about the definition of a vector
  • · Replies 8 ·
Replies
8
Views
2K
MHB Understanding the Constant Field of a Differential Field in $k((x))$
  • · Replies 1 ·
Replies
1
Views
2K
MHB Is the 3-D Rotation Matrix Defined by Euler Rotations or a General Angle?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Matrix Sum of Squares: Rotate Coord System to Express as Diagonal
  • · Replies 9 ·
Replies
9
Views
2K
MHB Short questions relating to field extensions
  • · Replies 9 ·
Replies
9
Views
2K
Vector Analysis using Basis Vectors
  • · Replies 5 ·
Replies
5
Views
2K
MHB Basic Exercise in Vector Spaces - Cooperstein Exercise 2, page 14
  • · Replies 5 ·
Replies
5
Views
2K
MHB Basic equation in Vector Space - Cooperstein Exercise 1, Section 1.3
  • · Replies 2 ·
Replies
2
Views
1K
Tensor Product Functor & Einstein Eqns: Relation?
  • · Replies 2 ·
Replies
2
Views
2K
Proving a set of vectors is linearly independent
  • · Replies 14 ·
Replies
14
Views
4K
MHB K[T]-Modules and Block Forms of Matrices
  • · Replies 4 ·
Replies
4
Views
2K
MHB Vector Spaces - The Space F^n - Cooperstein Exercise 12, page 10
  • · Replies 1 ·
Replies
1
Views
1K
How is the square of a transformed vector not a vector?
  • · Replies 7 ·
Replies
7
Views
2K
MHB Quantum Computing: Change of Basis
  • · Replies 5 ·
Replies
5
Views
3K
MHB Sums and Intersections of Submodules .... Berrick and Keating Exercise 1.2.12
  • · Replies 1 ·
Replies
1
Views
1K
MHB C[T] modules - Berrick and Keating Exercise 1.2.8 (c)
  • · Replies 4 ·
Replies
4
Views
2K
MHB Polynomials Acting on Spaces - B&K Ex. 1.2.2 (iv): An Intro by Peter
  • · Replies 7 ·
Replies
7
Views
2K
MHB Solver for Value of $a$: Unique, Infinite, No Solution
  • · Replies 4 ·
Replies
4
Views
2K
MHB Solving Systems of Equations with Whole Numbers
  • · Replies 1 ·
Replies
1
Views
1K
MHB Simple Notational Issue in Roman: "Advanced Linear Algebra"
  • · Replies 2 ·
Replies
2
Views
2K
Reduced Echelon Form - Which is correct?
  • · Replies 3 ·
Replies
3
Views
1K
Is Every Diagonalizable Endomorphism Defined by a Simple Polynomial?
  • · Replies 12 ·
Replies
12
Views
3K
MHB Is the Matrix Positive Definite?
  • · Replies 6 ·
Replies
6
Views
2K
Group Presentations Isomorphisms
  • · Replies 4 ·
Replies
4
Views
3K
When is the gram matrix positive definite?
  • · Replies 2 ·
Replies
2
Views
3K
A reasonable analogy for understanding similar matrices?
  • · Replies 4 ·
Replies
4
Views
3K
MHB How can we prove that k is an integer?
  • · Replies 8 ·
Replies
8
Views
2K
What Are the Subalgebras of Biquaternions?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Prove that there are infinitely many irreducible polynomials in Z5.
  • · Replies 3 ·
Replies
3
Views
3K
Coriolus effect, precession in 4+1D?
  • · Replies 1 ·
Replies
1
Views
1K
Simple fundamental subspaces problem stumping me
  • · Replies 3 ·
Replies
3
Views
1K
Polar and Jordan Decomp. in Intro to Linear Algebra?
  • · Replies 1 ·
Replies
1
Views
1K
What is meant by this statement?
  • · Replies 3 ·
Replies
3
Views
1K
Tricomplex numbers (Trinions anyone?)
  • · Replies 11 ·
Replies
11
Views
3K
Constraint on M to keep M^T * A * M positive semidefinite?
  • · Replies 2 ·
Replies
2
Views
1K
Insights Matrix Representations of Linear Transformations - Comments
  • · Replies 19 ·
Replies
19
Views
3K
Example of an algebra tensor product
  • · Replies 17 ·
Replies
17
Views
3K
The equivalence of a set and its permutations.
  • · Replies 3 ·
Replies
3
Views
1K
Transpose: a linear transformation?
  • · Replies 2 ·
Replies
2
Views
4K
MHB Interpreting & Solving Nullspace
  • · Replies 2 ·
Replies
2
Views
1K
MHB Proof that the solutions are algebraic functions
  • · Replies 1 ·
Replies
1
Views
1K
Difference between R^{4} and R^{1,3}
  • · Replies 1 ·
Replies
1
Views
1K
What Are the Fascinating Rotations of 3-Spheres in 4D Space?
  • · Replies 13 ·
Replies
13
Views
3K
What is the meaning of the term "dual"?
  • · Replies 15 ·
Replies
15
Views
2K
Why do we care about spin groups?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Why Are Eigenvalues and Eigenvectors Important in Linear Algebra?
  • · Replies 3 ·
Replies
3
Views
3K
Am I verifying that this is a group correctly?
  • · Replies 7 ·
Replies
7
Views
2K
Understanding the Role of Matrix Multiplication in Solving Equations
  • · Replies 2 ·
Replies
2
Views
1K
Is My SDP Formulation to Minimize trace((G^TG)^-1) Correct?
  • · Replies 1 ·
Replies
1
Views
1K
Verifying the Fourier Series is in Hilbert Space
  • · Replies 2 ·
Replies
2
Views
2K
MHB Show that the eigenvalues of any matrix are unaltered by a similarity transform
  • · Replies 17 ·
Replies
17
Views
7K
Lie group multiplication and Lie algebra commutation
  • · Replies 5 ·
Replies
5
Views
2K
Graphing Eigenvectors and Sine Curves: Understanding the Relationship
  • · Replies 9 ·
Replies
9
Views
2K
Backwards difference matrix divided by negative delta x?
  • · Replies 3 ·
Replies
3
Views
2K
Tensor in D-dimensional space crosswise with 2 vectors
  • · Replies 3 ·
Replies
3
Views
1K
Example of a factor space in physics
  • · Replies 10 ·
Replies
10
Views
2K
Simple showing inverse of matrix also upper triangular
  • · Replies 6 ·
Replies
6
Views
2K
MHB Inertia matrix from orbital angular momentum of the ith element (please check)
  • · Replies 3 ·
Replies
3
Views
2K
Deriving the structure constants of the SO(n) group
  • · Replies 9 ·
Replies
9
Views
4K
MHB Can Any Complex Matrix Be Decomposed into Hermitian and Skew-Hermitian Parts?
  • · Replies 5 ·
Replies
5
Views
3K
Deriving the commutation relations of the so(n) Lie algebra
  • · Replies 7 ·
Replies
7
Views
4K
MHB Understanding the Determinant of Commutator Matrices in Angular Momentum Systems
  • · Replies 5 ·
Replies
5
Views
3K
MHB How Do You Calculate the Determinant of a Matrix Using Index Notation?
  • · Replies 2 ·
Replies
2
Views
6K
MHB Did I Make a Mistake in Finding the Determinant of an Orthogonal 2x2 Matrix?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Uniqueness of Inverse Matrices: Proof and Explanation
  • · Replies 13 ·
Replies
13
Views
3K
Why are the eigenvectors the axes of an ellipse?
  • · Replies 1 ·
Replies
1
Views
9K
MHB Show determinant operator Det not linear
  • · Replies 6 ·
Replies
6
Views
2K
Dimension of SO(n) and its generators
  • · Replies 7 ·
Replies
7
Views
8K
Diff eqs with eigenvectors: double roots, but 2nd eigenvector?
  • · Replies 9 ·
Replies
9
Views
2K
MHB Null Column Vector vs $ |0 \rangle$
  • · Replies 1 ·
Replies
1
Views
2K
Diagonal Scaling of a 2x2 Positive Definite Matrix
  • · Replies 9 ·
Replies
9
Views
2K
MHB Proving the Pauli Matrix Identity with Ordinary Vectors: A Simplified Approach
  • · Replies 2 ·
Replies
2
Views
3K
MHB How to Prove the Lagrange Interpolation Formula?
  • · Replies 1 ·
Replies
1
Views
2K
LP objective function with unknown parameters
  • · Replies 4 ·
Replies
4
Views
2K
How Does the Jacobian Affect Coordinate Transformations?
  • · Replies 30 ·
2
Replies
30
Views
5K
A seemingly simple linear algebra equation that eludes me
  • · Replies 7 ·
Replies
7
Views
1K
MHB Artinian Rings - Comments by P.M. Cohn, Ring Theory, page 66
  • · Replies 4 ·
Replies
4
Views
2K
Group Theory why transformations of Hamiltonian are unitary?
  • · Replies 2 ·
Replies
2
Views
1K
Extremely confused on finding eigenvectors
  • · Replies 2 ·
Replies
2
Views
2K
What is the solution for a system of ODEs with a matrix coefficient?
  • · Replies 2 ·
Replies
2
Views
2K
Triangle inequality implies nonnegative scalar multiple
  • · Replies 3 ·
Replies
3
Views
2K
How helpful has the "algebra" been in understanding physics?
  • · Replies 6 ·
Replies
6
Views
2K
MHB Proving A is Zero Matrix if B is Invertible & Same Size as A
  • · Replies 1 ·
Replies
1
Views
2K
How can e^{Diag Matrix} not be an infinite series?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Calculating Determinant of $(N+1) \times (N+1)$ Matrix
  • · Replies 1 ·
Replies
1
Views
2K
Composition Series of Modules .... Remarks by Cohn
  • · Replies 5 ·
Replies
5
Views
2K
Noetherian Modules - Maximal Condition - Berrick and Keating
  • · Replies 12 ·
Replies
12
Views
3K
Thread: Artinian Modules - Cohn Exercise 3, Section 2.2, page 65
  • · Replies 1 ·
Replies
1
Views
2K
Corollary to Correspondence Theorem for Modules
  • · Replies 2 ·
Replies
2
Views
3K
MHB Parallel Forces in Cartesian Coordinates
  • · Replies 9 ·
Replies
9
Views
2K