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.
MHB Field Theory - Basic Theory - D&F Section 13.1
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Does a Linear Combination of Vectors in an Infinite Set Have to Be Finite?
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Solving Density Problems in Number Theory
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MHB Determinant Property: Seen it Before? True?
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MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 2, page 529
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MHB Field Theory - Algebrais Extensions - D&F - Section 13.2 - Exercise 4, page 530
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Some subset of a generating set is a basis
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Where Can I Find Linear Algebra Practice Problems for First Year Undergraduates?
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Is Every Finite Dimensional Lie Algebra Isomorphic to a Subalgebra of GL(n)?
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If f and g are orthogonal, are f* and g orthogonal?
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Cross product to find the area of a triangle
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Need help understanding Superposition Principle
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MHB Can someone solve this System, (1equation, 3 variables)
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MHB Algebraic Extensions: Dummit & Foote Section 13.2, Example 2 pg 526 - Help!
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Linearity of boolean expressions
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MHB Field Theory - Algebrais Extensions - Dummit and Foote Section 13.2
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If AB is invertible, then A and B are invertible.
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MHB Field Extensions - Dummit and Foote Chapter 13 - Exercise 2, page 519
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MHB Confused About Exercise 11 Answer Key
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What formula or principle governs this observed phenomena?
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MHB Spanning set of vectors question
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MHB Proof of Eigenvector Existence for Linear Maps on Finite-Dimensional Spaces
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Can a point view another point around an obstructing point?
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MHB Proof of a linear transformation not being onto
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MHB Proving Linear Maps are One-to-One
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MHB Field Theory - Dummit and Foote Ch 13 - Exercise 1, page 519
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MHB Solving a system of linear equations with one unknown value
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MHB 4x4 Matrix with rank B=4 and B^2=3
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MHB Field Extensions, Polynomial Rings and Eisenstein's Criterion
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MHB How Do D&F Derive \(a(x)(1 + x) + b(x)(x^3 - 2) = 1\)?
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MHB A linear transformation is invertible if and only if
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How Do Quaternions Enhance Understanding of 3D Rotations?
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Algebraic properites of the direct sum
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2 Rotations on different coordinate systems
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MHB Can You Find a Matrix with Ranking Requirements?
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MHB What is the expression for |c_n| in terms of the given matrice?
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Why Is the Dimension of the Solution Space n-r in Linear Algebra?
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Linear transformation from [-1,1] to [a,b]
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Solvable group: decomposable in prime order groups?
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MHB Problem involving matrix multiplication and dot product in one proof
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Equivalent statements to matrix A is orthogonal
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Should You Study All Proofs in Gallian's Abstract Algebra?
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Eigenstate to eigenstate evolution with no intermediate superposition?
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Linear Transformation: Does T(V) ⊆ W?
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Non-linear multivariable functions
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Looking for a proof regarding Baker-Campell-Hausdorff
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MHB Algebraic Geometry Basics for Understanding Tensegrity in Masters Thesis
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MHB Tensor notation for vector product proofs
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Roots and root vectors of sp(4,\mathbb{R})
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What Are the Benefits of Using Discrete Cosine Transform?
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Closure in Groups: Definition & Examples
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What Does Zero Empirical Mean in Data Matrices?
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How Does the Covariance Matrix Apply to Vectors X and Y?
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Proving the scalar matrices are the center of the matrix ring
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The sample covariance of N observations of K
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Extending the basis of a T-invariant subspace
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Question on conjugation closure of subgroups
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MHB What are the properties of orthogonal matrices?
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Direct sum of nullspace and range
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MHB Tricky Linear Algebra Question. To show that an operator is 'cyclic'.
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MHB Solving Householder Matrix Problem
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MHB Construct Orthogonal Basis in R^3: Solve Exercise
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Question about isomorphic mapping on direct sums?
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MHB Field Theory - Dummit and Foote - Chapter 13 - Theorem 6
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Is the Direct Sum Complement Unique?
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Graph Plane x+2y+3z=0 | Math Tutorials
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Sample mean and sample covariance
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Generating a vector space via a T-cyclic subspace
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What is the difference between Variance and Covariance?
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Inner Product on a Real Vector Space
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Quick question regarding isomorphic groups?
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MHB What is the proof for the residual sum of squares problem?
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MHB Inner product in n-dimensional vector space
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Square matrix to the power of a imaginary unit
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Is the geometric multiplicity of an eigenvalue a similar invariant?
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MHB Prove matrix has all real eigenvalues
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Way to re-express this equation by writing x and y separate?
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Linear Systems with pseudoinverse matrix using SVD
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Question regarding Kronecker Delta
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MHB Complex Conjugates/Proof by Induction
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MHB Automorphisms of the splitting field of the m-th cyclotomic polynomial.
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MHB Finitely Generated k-algebra - Nature of the finite generation - basic question
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MHB Can k(x) be Generated with Only One Rational Fraction?
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Transpose of the product of matrices problem
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Understanding the Relationship: Log, Traces, and Diagonalized Matrices
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Different ways to define vector multiplication?
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Are vectors assumed to be with respect to a standard basis?
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MHB Why Does Vector Norm Use "Double" Absolute Value?
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Filter Near-Zero Matrix Elements: Reasonable?
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Binomial formula for spherical tensors
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Recognizing even or odd permutation easily?
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Any pointer for analyzing this matrix?
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MHB Noetherian Rings - Dummit and Foote - Chapter 15 - Exercise 2a
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Linear Map T: Proving Existence of KerT=U if dimU≥dimV-dimW
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MHB Rings of the form R[X] - Ring Adjunction
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System of linear equation in term of column vector
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MHB Does Z[root(-3)] Qualify as a GCD Domain?
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What Is the Name of u=(3, 3, 3) Vector?
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Question about diagonalizable matrices
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MHB Question involving annihilators and solution spaces
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