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.
Finding integer numbers using basic operations
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Subalgebras of nipotent algebras
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Endomorphism ring over an elliptic curve
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High School Isn't the concept of a basis circular?
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Can the determinant of a combinatorial matrix be proven to always equal 1?
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Real and complex canonical forms
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Does the Factor (x+1) Affect Polynomial Coset Uniqueness in F_2[x]?
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Coordinate System Transformation
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What is the solution space for the equation 2^x - 5^y = 3 in modular arithmetic?
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What is the Matrix of a Non-Degenerate Non-Symmetric Bilinear Form?
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Eigenblades and the Geometric Algebra of Spinors
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Irreducible representation of so(3)
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Abel-Ruffini theorem: confusion regarding statement
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Undergrad Trying to get the point of some Group Theory Lemmas
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Local decomposition of unitary matrices
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Are p-adic fields isomorphic for different primes?
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Finding an f for 2^k+n: A Number Theory Problem
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MHB -m99.53 ty-plane hypotheses of Theorem 2.4.2.
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Representation of lie algebra of SL(2,C)
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What are efficient methods for solving A.x = b with a large sparse matrix?
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Orthogonal group over finite field
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Matrix Decomposition: Finding A & B for C & D
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How to make given numbers grassmann
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Can We Identify Quotient Groups as Subgroups of the Original Group?
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How to Align Kronecker Product Results with Scalar Elements in a Matrix?
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Cartan/Weyl basis. Please check I understand it properly
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Congruence Class - Proof of a number divisble by 7
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Numerical LA: Cholesky & Conjugate gradient method
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Can all polynomials in Z modulus 9 be written as the product of two polynomials?
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Three-Dimensional Matrix Multiplication
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Help with full rank factorization
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High School What are the properties of a quasigroup table?
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Linear least squares, condition number
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Highly ill-conditioned (close to singular) linear problem
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MHB Problem (c) for Discrete Value Ring
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Undergrad Determining coefficients from an equation with 3 variables
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MHB 1.3.11 Determine if b is a linear combination
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Undergrad "Map" point between coordinate systems
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Givens rotations versus Euler angles
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Implicit function for arbitrary cylinder
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How Can 2D Plane Coordinates Be Transformed into 3D Coordinates?
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Finding a Complex Conjugate value of wave function
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A positive definite Hermitian Form
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Vector problem involving velocity and wind
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Approximate Ratio: Steps to Find Reasonable Solutions
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Fibonacci Rectangles and Triangular Numbers
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Maximal left ideal of matrix ring
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What is a Tensor Product and How Does it Relate to Vectors and Matrices?
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Semisimple algebra (Killing form)
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Undergrad Element-wise square root of a vector notation?
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Undergrad Simplifying a matrix into an equation
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Undergrad Question about an eigenvalue problem: range space
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Graduate What Is the Significance of the Matrix Identity Involving \( S^{-1}_{ij} \)?
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Undergrad Finding the Matrix O for a 4x4 Operator Acting on a 4x1 Vector
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Undergrad Linear transformation T: R3 -> R2
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MHB Discrete valuation Ring which is a subring of a field K Problem
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Graduate How do I find the change of basis matrix for the JCF of M?
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Weil's Conjectures and Grothendieck's Standard Conjectures
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Prooving the Cayley-Hamilton Theorem
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How Are Pell and Sophie Germain Triangular Numbers Related?
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Calculating Components of 4D Fully Antisymmetric Tensor
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Shift and convolution in matrix form
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Properties of 4x4 symmetric matrix with eigvals E1, -E1, E2, -E2
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What is the Geometric Interpretation of the Final Step in SVD?
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Complex conjugate variables as independent variables in polynomial equations
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Condition number (or estimate) of a very large matrix
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Question about Direction Cosine Matrix
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All the ways to build positive definite matrices
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MHB Markov Process Limit: Calculating $u_k$ as a Function of $a,b$
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Rotation of Elipse axes from covariance matrix
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What is the general algorithm for computing the null space of a 3x3 matrix?
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Undergrad Linear Transformations: Why w1 is a Linear Combination of v
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MHB Does a Line Intersect a Polygon?
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Undergrad Solving 2 equations and 2 unknowns with vectors
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MHB 17.1 Determine if T is a linear transformation
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MHB 16.1 Show that e^{2x}, sin(2x) is linearly independent on + infinity -infinity
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Diagonalizability of a matrix containing smaller diagonalizable matrices
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Is there a connection between Borges' 'El Aleph' and Aleph0, C, and F?
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MHB Find Inner Product for Quadratic Form in R^3
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Undergrad Finding a linear combination to enter a sphere
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Quadratic eigenvalue problem and solution (solved in Mathematica)
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MHB 14.3 Find a basis for NS(A) and dim{NS(A)}
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MHB 14.2 find a basis for NS(A) and dim{NS(A)}
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MHB Linear Transformations: Proving Rules & Demonstration
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MHB 13.2 verify that ....... is a basis for R^2 find [v]_beta
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MHB 14.1 find a vector v that will satisfy the system
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MHB 12.6 linearly dependent or linearly independent?
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MHB Are These Vectors Linearly Dependent?
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Undergrad Confusion about the Direct Sum of Subspaces
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Undergrad Linear Algebra - Inner Product problem
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MHB 11.1 Determine if the polynominal.... is the span of (....,....)
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Undergrad Does a unitary matrix have such property?
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MHB 10.3 Determine if A is in the span B
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Undergrad Linear least squares regression for model matrix identification
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MHB 10.2 Determine if the set of vectors form a vector space
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MHB -307.17.1 Show that S and T are both linear transformations
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Undergrad Mistake in Schaum's Group Theory?
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MHB Either or statement from Abstract Algebra Book
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MHB Solving Nilpotent Problem in Abstract Algebra
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MHB Practice Test Solutions: Derivation of [ -4/3, 1/3, 1 ] with Red Correction
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