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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 Understand Theorem 2.15 - Bruce Cooperstein's Advanced Linear Algebra
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MHB Correspondence Theorem for Vector Spaces - Cooperstein Theorem 2.15
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Graduate Calculating Square Root of a Matrix in Quantum Information Theory
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MHB Can this system of equations be solved analytically?
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Undergrad Can an orthogonal matrix be complex?
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MHB What is the Simplest Form of a Field Extension of the Reals?
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MHB Vector Spaces and Linear Transformations - Cooperstein Theorem 2.7
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Graduate What are the elements of Lie algebra in the case of a single generator?
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MHB Is V a Subspace of P2?
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Undergrad Why are linear equations usually written down as matrices?
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MHB Prove F(a,b)=F(a)(b)=F(b)(a) in Field Extensions
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Graduate Factorization of floor functions of fractions
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Undergrad Ellipse Rotation: Solving with Normal Rotation Matrix
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MHB Roots of an irreducible polynomial over a finite field
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Undergrad Can a 3x3 Matrix Represent a Quadratic, Cubic, or Quartic Function?
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MHB Finding Eigenvalues of Matrix A: Wrong Answer, What Am I Doing Wrong?
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Graduate Local Algebra: intersection multiplicity
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Undergrad Why Do Different Definitions of Rotation Matrices Exist in Mathematics?
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Graduate Where Am I Going Wrong in My Category Theory Solution?
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MHB Vector Spaces - The Exchange Theorem - Cooperstein Theorem 1.16
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Undergrad Euler Representation of complex numbers
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Graduate Nonlinear coordinate transformation
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Graduate Is My Approach to Matrix Exponentiation Valid?
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High School I have a question about the definition of a vector
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MHB Understanding the Constant Field of a Differential Field in $k((x))$
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MHB Is the 3-D Rotation Matrix Defined by Euler Rotations or a General Angle?
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MHB Matrix Sum of Squares: Rotate Coord System to Express as Diagonal
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MHB Short questions relating to field extensions
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Undergrad Vector Analysis using Basis Vectors
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MHB Basic Exercise in Vector Spaces - Cooperstein Exercise 2, page 14
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MHB Basic equation in Vector Space - Cooperstein Exercise 1, Section 1.3
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Graduate Tensor Product Functor & Einstein Eqns: Relation?
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Undergrad Proving a set of vectors is linearly independent
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MHB K[T]-Modules and Block Forms of Matrices
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MHB Vector Spaces - The Space F^n - Cooperstein Exercise 12, page 10
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Undergrad How is the square of a transformed vector not a vector?
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MHB Quantum Computing: Change of Basis
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MHB Sums and Intersections of Submodules .... Berrick and Keating Exercise 1.2.12
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MHB C[T] modules - Berrick and Keating Exercise 1.2.8 (c)
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MHB Polynomials Acting on Spaces - B&K Ex. 1.2.2 (iv): An Intro by Peter
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MHB Solver for Value of $a$: Unique, Infinite, No Solution
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MHB Solving Systems of Equations with Whole Numbers
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MHB Simple Notational Issue in Roman: "Advanced Linear Algebra"
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Undergrad Reduced Echelon Form - Which is correct?
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Undergrad Eigenvectors and Row/Column Vectors: What's the Connection?
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Graduate Is Every Diagonalizable Endomorphism Defined by a Simple Polynomial?
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Graduate Over constrained least squares analysis
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Undergrad Can Gauss-Jordan Elimination simplify a matrix into a reduced row echelon form?
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MHB Is the Matrix Positive Definite?
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MHB Finding Unique solution for system of linear equations
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Graduate Group Presentations Isomorphisms
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Graduate When is the gram matrix positive definite?
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Graduate A reasonable analogy for understanding similar matrices?
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MHB How can we prove that k is an integer?
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Graduate What Are the Subalgebras of Biquaternions?
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MHB Prove that there are infinitely many irreducible polynomials in Z5.
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Graduate Coriolus effect, precession in 4+1D?
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Undergrad Simple fundamental subspaces problem stumping me
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Undergrad Polar and Jordan Decomp. in Intro to Linear Algebra?
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Graduate What is meant by this statement?
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Graduate Tricomplex numbers (Trinions anyone?)
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Graduate Constraint on M to keep M^T * A * M positive semidefinite?
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Insights Matrix Representations of Linear Transformations - Comments
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Graduate Example of an algebra tensor product
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Graduate The equivalence of a set and its permutations.
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Undergrad Transpose: a linear transformation?
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MHB Interpreting & Solving Nullspace
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MHB Proof that the solutions are algebraic functions
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Graduate Difference between R^{4} and R^{1,3}
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Graduate What Are the Fascinating Rotations of 3-Spheres in 4D Space?
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Graduate What is the meaning of the term "dual"?
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Graduate Why do we care about spin groups?
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MHB Why Are Eigenvalues and Eigenvectors Important in Linear Algebra?
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Graduate Am I verifying that this is a group correctly?
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Undergrad Understanding the Role of Matrix Multiplication in Solving Equations
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Graduate Is My SDP Formulation to Minimize trace((G^TG)^-1) Correct?
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Graduate Verifying the Fourier Series is in Hilbert Space
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MHB Show that the eigenvalues of any matrix are unaltered by a similarity transform
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Graduate Lie group multiplication and Lie algebra commutation
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Graduate Graphing Eigenvectors and Sine Curves: Understanding the Relationship
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Graduate Backwards difference matrix divided by negative delta x?
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Graduate Tensor in D-dimensional space crosswise with 2 vectors
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MHB What is the Dot Product of u+v?
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Graduate Example of a factor space in physics
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Undergrad Simple showing inverse of matrix also upper triangular
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MHB Inertia matrix from orbital angular momentum of the ith element (please check)
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Graduate Deriving the structure constants of the SO(n) group
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MHB Can Any Complex Matrix Be Decomposed into Hermitian and Skew-Hermitian Parts?
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Graduate Deriving the commutation relations of the so(n) Lie algebra
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MHB Understanding the Determinant of Commutator Matrices in Angular Momentum Systems
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MHB How Do You Calculate the Determinant of a Matrix Using Index Notation?
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MHB Did I Make a Mistake in Finding the Determinant of an Orthogonal 2x2 Matrix?
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Graduate Can Matrix Determinants Be Used to Find Optimal Area in Higher Dimensions?
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MHB Uniqueness of Inverse Matrices: Proof and Explanation
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Graduate Why are the eigenvectors the axes of an ellipse?
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MHB Show determinant operator Det not linear
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Graduate Dimension of SO(n) and its generators
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Graduate Diff eqs with eigenvectors: double roots, but 2nd eigenvector?
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MHB Null Column Vector vs $ |0 \rangle$
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Graduate Diagonal Scaling of a 2x2 Positive Definite Matrix
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