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.
Undergrad Is the Frobenius Norm a Reliable Indicator of Matrix Conditioning?
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MHB Smallest subfield of C that contains i
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Undergrad How to check if a matrix is Hilbert space and unitary?
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High School Why does a matrix diagonalise in this case?
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Graduate Commutation and Non-Linear Operators
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Undergrad How to study an ODE in matrix form in a Hilbert space?
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MHB Eigenvector Calculations and Verification for y1+y2=5
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MHB Questions about analysis of algorithm
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Undergrad Bases, operators and eigenvectors
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Undergrad Doubt about proof on self-adjoint operators.
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Insights What Are Eigenvectors and Eigenvalues? - Comments
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Undergrad What is the equivalent of a group in category theory?
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Undergrad How many generators can a cyclic group have by definition?
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Undergrad Why can't a set of vectors with less than n elements span ℝn?
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Undergrad Notation for systems of simultaneous equations
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Undergrad How to find the matrix of the derivative endomorphism?
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Graduate On the equivalent definitions for solvable groups
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Undergrad Can a shear operation introduce a new linear dependency?
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Undergrad Help Needed: Understanding Hungerford's Algebra Book Proofs
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Undergrad What is the definition of a matrix in function form?
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MHB How does the row picture differ from the column picture in linear systems?
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Insights What Is a Tensor? The mathematical point of view
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Undergrad Terminology involving "homomorphic"
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MHB What Is Required to Prove a Subset is a Vector Space?
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Undergrad Groups of Automorphisms - Aut(C) ....
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Undergrad Groups of Automporphisms - remarks by Anderson and Feil ....
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Undergrad Understanding Quaternion Transformations for 3D Vectors
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Undergrad How can there only be two possible four-element groups?
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Undergrad Are my thoughts about groups correct?
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Why does Gaussian elimination work?
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High School Define Vector on x-Axis: -d/2 to d/2
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Undergrad Linear Program:Multiple Optima for multivariable Obj. Func.?
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Undergrad Question about group representation
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Undergrad Exterior Algebra: (A1−A2,B1−B2,C1−C2) ∧ (A1,B1,C1) Explained
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Undergrad Eigenvalues of Circulant matrices
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Finding Eigenvectors with Lanczos Algorithm
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MHB Using the First Property to Prove the Second Property of the Exterior Product
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MHB Understand Proof for Exterior Product Proposition
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Undergrad Is Euclidean Space Inherently Geometric or Just a Vector Space?
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Undergrad Is My Panel Data Sample Size Adequate and Modeling Approach Correct?
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Undergrad Finding the Kernel of a Matrix Map
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Undergrad Solving System of Equations w/ Gauss-Jordan Elimination
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Undergrad Matrix for transforming vector components under rotation
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Undergrad Homomorphism of an elementwise sum and dot product
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Undergrad How Do Eigenvalues of Block Matrices Relate to Their Sub-Matrices and Graphs?
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Undergrad Transforming a Matrix: Elementary Methods for Finite Fields
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High School Vector Proof: Solving for IuI and IvI using Dot Product Properties
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Gershgorin Circle Theorem, mathematical derivation of eigenvalue estimates
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Graduate Numerically Calculating Eigenvalues
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Undergrad Solving a system of linear equations using back substitution
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Undergrad Addition of exponents proof in group theory
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Graduate Understanding Rank of a Matrix: Important Theorem and Demonstration
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Undergrad Inner Product vs. Dot Product Confusion in Quantum Physics?
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Graduate Transformation of the neighborhood of a branch point
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High School Generalized Linear equation of a cube
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High School How Do Rotation Matrices Impact Coordinate Systems and Object Transformations?
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Graduate Selected solution of linear equations
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Undergrad Lie Algebra states of a representation
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Undergrad Normal modes using representation theory
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Undergrad Finite and infinitesimal Rotations
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Undergrad Advantages of Vector Spaces over Modules
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Undergrad Matrix Equation -- clarification about solving a system
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Undergrad How do I know if a matrix is positive definite?
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Graduate Algebraic structure in time evolution
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Undergrad Need help solving for X in third order polynomial
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Undergrad SU(2) Generators: Understanding Lie Algebra
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Graduate If [A,B]=0, are they both functions of some other operator?
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Undergrad Index (killing form ?) in a reducible representation
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Graduate How to Calculate the Rotation Axis Incorporating Translation?
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MHB When does a reflection around a point result in a reflection along a line?
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Graduate How to prove The Cayley-Hamilton Theorem?
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Undergrad Proving Matrix Exponential Theorem: Unipotent & Nilpotent
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Graduate Summing simple histograms to recreate a more complex one
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MHB How can we determine the reflection across a given line in Hesse normal form?
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MHB Analyzing the Composition of Scalings with Different Centers and Scaling Factors
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MHB Conditions so that the determinant is zero
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MHB Mappings - Similarity transformations
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MHB What Are the Key Properties of Reflections, Rotations, and Similitude Mappings?
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Undergrad Nice intro to connections between algebra and geometry
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MHB Rotation around an arbitrary point
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MHB Finding the Centroid of a Triangle Using Coordinates
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MHB Find XYZ for Tip of Vector Given Info on 2 Other Vectors w/ Tails at Same Point
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MHB How Do You Find the Equation of a Polar Line for a Circle with Given Points?
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MHB How to Calculate the Distance Between Parallel Lines in Hesse Normal Form?
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MHB How to Calculate the Equation of a Tangent Line to a Circle?
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Graduate Getting as close as possible to a solution (system of equations)?
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High School Galois Groups .... A&F Example 47.7 .... ....
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MHB Galois Groups .... A&F Example 47.7 .... ....
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MHB Groups of Automorphisms - remarks by Anderson and Feil ....
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MHB Galois Groups .... A&W Theorem 47.1 .... ....
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Undergrad Galois Groups .... A&W Theorem 47.1 .... ....
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MHB Groups of Automporphisms - Aut(C) .... Anderson and Feil Ch. 24 ....
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Undergrad Finite Extensions - A&F Example 44.2 .... ....
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MHB Basic Notation for Field Extensions .... ....
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MHB Finite Extensions - A&F Example 44.2 .... ....
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Undergrad Why is there a Matrix A that satisfies F(x,y)=<Ax,y>?
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MHB Change from cartesian coordinates to cylindrical and spherical
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Dot Product of Streaming vectors
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Undergrad Splitting Fields: Anderson and Feil, Theorem 45.6 ....
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MHB Splitting Fields: Anderson and Feil, Theorem 45.6 ....
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