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.
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Vector or Parametric Form of the Equation of a Plane P
- Math Amateur
- · Replies 4 ·
Undergrad How to determine the smallest subspace?
- maNoFchangE
- · Replies 5 ·
Linear Applications: Electrical Networks
- Pull and Twist
- · Replies 1 ·
Prove Abelian Group: $(a \cdot b)^n = a^n \cdot b^n$
- Guest2
- · Replies 1 ·
Two Versions of the Correspondence Theorem for Vector Spaces
- Math Amateur
- · Replies 4 ·
Sum of Two Subspaces and lub - Roman, Chapter 1, page 39
- Math Amateur
- · Replies 2 ·
Graduate Understanding Equivariant Maps in Group Theory
- mnb96
- · Replies 8 ·
Graduate Understanding POVMs and Quantum Information in Corollary Proofs
- aaaa202
- · Replies 1 ·
Understand Theorem 2.15 - Bruce Cooperstein's Advanced Linear Algebra
- Math Amateur
- · Replies 1 ·
Correspondence Theorem for Vector Spaces - Cooperstein Theorem 2.15
- Math Amateur
- · Replies 2 ·
Graduate Calculating Square Root of a Matrix in Quantum Information Theory
- aaaa202
- · Replies 10 ·
Can this system of equations be solved analytically?
- Siron
- · Replies 3 ·
Undergrad Can an orthogonal matrix be complex?
- charlies1902
- · Replies 9 ·
What is the Simplest Form of a Field Extension of the Reals?
- Kiwi1
- · Replies 2 ·
Vector Spaces and Linear Transformations - Cooperstein Theorem 2.7
- Math Amateur
- · Replies 5 ·
Graduate What are the elements of Lie algebra in the case of a single generator?
- LagrangeEuler
- · Replies 11 ·
Is V a Subspace of P2?
- rayne1
- · Replies 3 ·
Undergrad Why are linear equations usually written down as matrices?
- japplepie
- · Replies 4 ·
Prove F(a,b)=F(a)(b)=F(b)(a) in Field Extensions
- Scherie
- · Replies 3 ·
Graduate Factorization of floor functions of fractions
- DirichletHole
- · Replies 4 ·
Undergrad How do I rotate an ellipse using a rotation matrix?
- Physgeek64
- · Replies 12 ·
Roots of an irreducible polynomial over a finite field
- Scherie
- · Replies 1 ·
Undergrad Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?
- Bruno Tolentino
- · Replies 3 ·
Eigenvalues of a 3×3 matrix with parameter k
- Yankel
- · Replies 3 ·
Graduate Why is intersection multiplicity the Euler characteristic, not the dimension?
- giulio_hep
- · Replies 14 ·
Undergrad Why Do Different Definitions of Rotation Matrices Exist in Mathematics?
- LagrangeEuler
- · Replies 6 ·
Graduate Error in my category theory solution from Basic Homological Algebra
- nateHI
- · Replies 6 ·
Vector Spaces - The Exchange Theorem - Cooperstein Theorem 1.16
- Math Amateur
- · Replies 7 ·
Undergrad Euler Representation of complex numbers
- Hijaz Aslam
- · Replies 6 ·
Graduate Coordinate transformation to map slanted boundaries to constant lines
- shawnstrausser
- · Replies 1 ·
Graduate Is My Approach to Matrix Exponentiation Valid?
- DuckAmuck
- · Replies 3 ·
High School Why can vectors be expressed as linear combinations of unit vectors?
- Chump
- · Replies 8 ·
What is the constant field of a differential field?
- mathmari
- · Replies 1 ·
Is the 3-D Rotation Matrix Defined by Euler Rotations or a General Angle?
- ognik
- · Replies 3 ·
Matrix Sum of Squares: Rotate Coord System to Express as Diagonal
- ognik
- · Replies 9 ·
Short questions relating to field extensions
- Kiwi1
- · Replies 9 ·
Undergrad Vector Analysis using Basis Vectors
- Jimmy87
- · Replies 5 ·
Cooperstein section 1.3 exercise 2 on vector spaces
- Math Amateur
- · Replies 5 ·
Cooperstein Exercise 1, Section 1.3: vector space axioms
- Math Amateur
- · Replies 2 ·
Graduate What is the relationship between tensor product functors and the Einstein equations?
- nateHI
- · Replies 2 ·
Undergrad Proving a set of vectors is linearly independent
- BillhB
- · Replies 14 ·
K[T]-Modules and Block Forms of Matrices
- Math Amateur
- · Replies 4 ·
Cooperstein exercise 12: solving a linear equation in F^2 mod 5
- Math Amateur
- · Replies 1 ·
Undergrad How is the square of a transformed vector not a vector?
- BHL 20
- · Replies 7 ·
Relating matrix representations under basis change with unitary transformation
- Ackbach
- · Replies 5 ·
Berrick and Keating Exercise 1.2.12 on submodule sums and intersections
- Math Amateur
- · Replies 1 ·
C[T] module structure on C³ with nilpotent matrix A
- Math Amateur
- · Replies 4 ·
Why use indeterminate T in B&K example 1.2.2 (iv)
- Math Amateur
- · Replies 7 ·
Solver for Value of $a$: Unique, Infinite, No Solution
- evinda
- · Replies 4 ·
Solving Systems of Equations with Whole Numbers
- Yankel
- · Replies 1 ·
Simple Notational Issue in Roman: "Advanced Linear Algebra"
- Math Amateur
- · Replies 2 ·
Undergrad Reduced Echelon Form - Which is correct?
- L = K - U
- · Replies 3 ·
Undergrad Eigenvectors and Row/Column Vectors: What's the Connection?
- Mappe
- · Replies 3 ·
Graduate Is Every Diagonalizable Endomorphism Defined by a Simple Polynomial?
- geoffrey159
- · Replies 12 ·
Graduate Over constrained least squares analysis
- benzun_1999
- · Replies 3 ·
Undergrad Can Gauss-Jordan Elimination simplify a matrix into a reduced row echelon form?
- askor
- · Replies 16 ·
Is the Matrix Positive Definite?
- evinda
- · Replies 6 ·
Finding Unique solution for system of linear equations
- diggybob
- · Replies 1 ·
Graduate Group Presentations Isomorphisms
- MostlyHarmless
- · Replies 4 ·
Graduate When is the gram matrix positive definite?
- perplexabot
- · Replies 2 ·
Graduate A reasonable analogy for understanding similar matrices?
- kostoglotov
- · Replies 4 ·
How can we prove that k is an integer?
- mathmari
- · Replies 8 ·
Graduate What Are the Subalgebras of Biquaternions?
- EinsteinKreuz
- · Replies 2 ·
Prove that there are infinitely many irreducible polynomials in Z5.
- Kiwi1
- · Replies 3 ·
Graduate Coriolus effect, precession in 4+1D?
- Hornbein
- · Replies 1 ·
Undergrad Simple fundamental subspaces problem stumping me
- kostoglotov
- · Replies 3 ·
Undergrad Polar and Jordan Decomp. in Intro to Linear Algebra?
- kostoglotov
- · Replies 1 ·
Graduate What is meant by this statement?
- Amany Gouda
- · Replies 3 ·
Graduate Tricomplex numbers with i² = j² = ij = -1
- EinsteinKreuz
- · Replies 11 ·
Graduate Constraint on M to keep M^T * A * M positive semidefinite?
- perplexabot
- · Replies 2 ·
Insights Matrix Representations of Linear Transformations - Comments
- Fredrik
- · Replies 19 ·
Graduate Example of an algebra tensor product
- Geofleur
- · Replies 17 ·
Graduate The equivalence of a set and its permutations.
- Odious Suspect
- · Replies 3 ·
Undergrad Transpose: a linear transformation?
- kostoglotov
- · Replies 2 ·
Finding the nullspace of a 3×3 matrix in parametric form
- cbarker1
- · Replies 2 ·
Proof that the solutions are algebraic functions
- mathmari
- · Replies 1 ·
Graduate Difference between R^{4} and R^{1,3}
- spaghetti3451
- · Replies 1 ·
Graduate What Are the Fascinating Rotations of 3-Spheres in 4D Space?
- Hornbein
- · Replies 13 ·
Graduate What is the meaning of the term "dual"?
- "Don't panic!"
- · Replies 15 ·
Graduate Why do we care about spin groups?
- Apogee
- · Replies 1 ·
Why Are Eigenvalues and Eigenvectors Important in Linear Algebra?
- Yankel
- · Replies 3 ·
Graduate Am I verifying that this is a group correctly?
- gavin123
- · Replies 7 ·
Undergrad How does x appear in going from equation 3 to 4?
- Martin V.
- · Replies 2 ·
Graduate Is My SDP Formulation to Minimize trace((G^TG)^-1) Correct?
- perplexabot
- · Replies 1 ·
Graduate Verifying the Fourier Series is in Hilbert Space
- kostoglotov
- · Replies 2 ·
Show that the eigenvalues of any matrix are unaltered by a similarity transform
- ognik
- · Replies 17 ·
Graduate Lie group multiplication and Lie algebra commutation
- spaghetti3451
- · Replies 5 ·
Graduate How do eigenvectors of a difference matrix relate to sine curves?
- kostoglotov
- · Replies 9 ·
Graduate Backwards difference matrix divided by negative delta x?
- kostoglotov
- · Replies 3 ·
Graduate Tensor in D-dimensional space crosswise with 2 vectors
- olgerm
- · Replies 3 ·
What is the Dot Product of u+v?
- karush
- · Replies 3 ·
Graduate Example of a factor space in physics
- Geofleur
- · Replies 10 ·
Undergrad Simple showing inverse of matrix also upper triangular
- snrwww
- · Replies 6 ·
Deriving inertia matrix from orbital angular momentum with bac-cab rule
- ognik
- · Replies 3 ·
Graduate Deriving the structure constants of the SO(n) group
- spaghetti3451
- · Replies 9 ·
Can Any Complex Matrix Be Decomposed into Hermitian and Skew-Hermitian Parts?
- ognik
- · Replies 5 ·
Graduate Deriving the commutation relations of the so(n) Lie algebra
- spaghetti3451
- · Replies 7 ·
Why does Det([J_x, J_y]) = i Det(J_z) not work?
- ognik
- · Replies 5 ·
How Do You Calculate the Determinant of a Matrix Using Index Notation?
- ognik
- · Replies 2 ·
General form of orthogonal 2x2 matrices with determinant ±1
- ognik
- · Replies 8 ·