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 Types of complex matrices, why only 3?
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Undergrad A different way to express the span
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Graduate How to prove vector identities WITHOUT using levi civita ?
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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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MHB Proving the Equality of A and B: A+B=0 or A=B
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Undergrad Bases, operators and eigenvectors
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Undergrad What does this vector notation mean?
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Undergrad Can a Hermitian matrix have complex eigenvalues?
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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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MHB How to Find the Zeros Using the Rational Roots Theorem?
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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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Undergrad 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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MHB Calculating Ratio of Determinants for $a,b$ Real Coefficients
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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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Graduate 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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Graduate Infinite Basis and Supernatural Numbers
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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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Graduate 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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High School Looking for some intuition on a basic Algebra equation
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Undergrad How can -a be equal to (-1)*a?
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High School What is the requirement for something to qualify as vector?
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Undergrad Are there relations that are valid for any field?
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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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Undergrad Spectral Bisection of Simplest Graph Clearly Incorrect
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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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MHB Hcc8.12 Find the sum of vectors
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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 Is zero vector always present in any n-dimensional space?
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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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Undergrad Injectivity equivalent to having a left inverse
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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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