Linear and Abstract Algebra Forum

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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.
Graduate Proof that eigenvalues are constants
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MHB Could you explain me about 'relation algebraic property with conjugate'?
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Undergrad Complex numbers and vector multiplies continued
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Graduate Relationship between inverse matrix and inertia tensor?
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MHB Determinant - Proof for distinct real numbers
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MHB Proof: Determinant of 3 Non-Colinear Points is 0
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MHB What is Algebraic Multiplicity and How Does It Relate to Solving Matrices?
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MHB What is the basis for $F$ in linear algebra?
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MHB Finding a basis for a Vector Space
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Graduate Why does this shortcut for eigenvectors of 2x2 symmetric work?
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Graduate Scaling the parameter of the SO(2) rotation matrix
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Graduate Representations of semi-simple lie algebra
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Graduate Computing the Inverse of a Cubic Matrix
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MHB Squares in a field with q^n elements
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Graduate Large weighted least squares system
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Graduate Vector Identity: Understanding ∇⋅A and A ⋅∇ in Spherical Coordinates
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Undergrad Matrix Differentiation Problem
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Undergrad Stumbling Upon Pi: Could a Billion 3's be Hidden Inside?
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Undergrad 4th order Polynomail starting at a desired Point
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Graduate Jacobi and Gauss-Seidel Iteration
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Undergrad How to find a point on line of intersection of 2 planes?
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MHB Algebra help about polynomials
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Graduate Transforming Vectors from Basis B to C: A Confusing Matter
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MHB Vector that describes the power
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MHB Find the minimal polynomial of some value a over Q
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Graduate Algebraic Multiplicity of an Eigenvalue
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Graduate A lemma in proving Sylow's theorem
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MHB Show eigenvalues are real and positive (too easy?)
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MHB Can a vector space also be a set?
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Undergrad How Did Abstract Algebra Evolve From Elementary Algebra?
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MHB Prove One-to-One Correspondence Conjugate Subgroups & Cosets N
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MHB What is the General Pattern for Finding Matrix Powers?
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Graduate Confusion with Tensors: Understanding Finite-Dimensional Vector Spaces
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Graduate Unraveling Theorem 4.2.5: Understanding Linear Maps and Scalar Products
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Graduate Operators for comparing superposition components -- definable?
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MHB Antisymmetry Invariant Under Similarity Orthogonal Transforms
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MHB Product of Symmetric and Antisymmetric Matrix
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MHB How Do You Prove (det A)aij = Cij(A) for an Orthogonal Matrix with det(A)=+1?
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Graduate Can the system response function be calculated?
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Graduate Two quotient groups implying Cartesian product?
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MHB Question about the "E" Lie algebras
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Undergrad Eigenvalues and diagonalization of a matrix
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MHB Can a Non-Integer Exponent be Used to Solve a Polynomial Equation?
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Graduate Least Square Estimator for Matrices: Bill's Problem
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Undergrad How Does the Vector Field F = [-x³, x, 0] Behave for Constant x Values?
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Undergrad How to Solve a Vector Equation with Doubts on the Solution?
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MHB Is 1, α, α², ..., αⁿ⁻¹ a Basis for ℚ(α)?
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MHB What Are the Bases for Column and Null Spaces of These Matrices?
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MHB Direct sum of p-primary components of an R-module counterexample?
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Graduate Solution to vector equation involving vector product
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Undergrad What is the necessary condition for matrix commutation?
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Graduate Finding the points of a cube given two points.
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MHB Inverse image of a set under the restriction of a function
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MHB Proving elipsoide radius of axis i equals 1/sqrt(λi)
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MHB Proving that a module can be decomposed as a direct sum of submodules
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Graduate When n*(n+1)/2 - k is never a square
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MHB Clarification for Alternating Group
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MHB Finding inverse of F in Munkres' Topology Ch.2 EX 5 pg 106
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Graduate What does it mean to say a Lie group is real?
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MHB Definition of matrix transformation
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Graduate Matrix of Gradients: Notation Explained
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MHB Relation between null and column space
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MHB Eigenvector of 3x3 matrix with complex eigenvalues
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MHB Injective and surjective functions
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MHB General orthogonal scale factor identity
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Undergrad Looking for an example of a Successive over-relaxation
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Graduate Why Doesn't This Theorem Hold in Real Vector Spaces?
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MHB Basis for $U$ using $\operatorname{null}A$
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Undergrad System of homogeneous equations
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Graduate Is sl(3,R) a subalgebra of sp(4,R)?
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Undergrad Euler's identity, mathematical beauty and applications of it
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MHB Is a Matrix Invertible and Have Integer Entries If Its Determinant is 1 or -1?
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Undergrad How to Solve Equations with a Singular Matrix?
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MHB Determinant of Block Matrices: How Do Non-Zero Blocks Affect the Determinant?
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MHB Why Is My Determinant Calculation Using Upper Triangular Form Incorrect?
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Graduate How Do You Find a Basis for the Orthogonal Complement of Given Vectors in ℝ5?
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MHB Natural Isomorphism b/w Dual Spaces Tensor Prod & Multilinear Form Space
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Graduate Block diagonalization of a matrix
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High School Proof of (A+B)^2 = A^2 + 2AB + B^2 for Matrix Algebra
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Undergrad Test Tomorrow Linear independence, spanning, basis
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MHB If matrix lambda is diagonal with entries 0,1 then lambda squared is lambda
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Undergrad Understand Linear Algebra: Im(BF) in Im(B)?
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High School Difference between REF/RREF (Gauss vs Gauss-Jordan)?
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MHB Barycentric coordinates in a triangle - proof
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Graduate Coefficients on the p-adic expansions
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Graduate P-adic norm, valuation, and expansion
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Graduate Uncovering Surprising Properties of the Cholesky Decomposition
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Graduate How to Simplify a Double Dot Product of Tensors?
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Graduate Constructing a field of 4 elements
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Graduate Su(2), so(3) and their representations
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Undergrad QR Decomposition w/ Householder and Givens Transformations
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Graduate Double Dot Product: Solving 3D Vector Problem
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Graduate Green's Function - modified operator
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Undergrad Matrices and systems of equations
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Graduate What are some real-world applications of cyclic groups and Galois fields?
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Graduate Struggling to understand a field theorm's corollary
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Graduate Every field contains a copy of Z_p
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MHB Matrices Show that Tr(A + B) = Tr(A) + Tr(B).
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MHB Find a Basis for U with $\text{rref}(A)$
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Graduate Trouble understanding simple Galois Theory example
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