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 What Are the Elements of (Z4×Z12)/<2,1>?
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Undergrad How can I rotate a vector in 3D to match another vector's rotation?
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Undergrad Finite fields, irreducible polynomial and minimal polynomial theorem
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Undergrad Showing a set is a basis for a vector space
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Undergrad Subgroup axioms for a symmetric group
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Undergrad Why should a Fourier transform not be a change of basis?
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MHB Group Homomorphism: True or False?
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Undergrad Understanding the concepts of isometric basis and musical isomorphism
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High School Simple question about the dual space
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Undergrad Scalar powers of a matrix exponential
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MHB Find Point D on Plane for 4 Unit Cube Pyramid
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MHB How Does the Composite Transformation H Affect a Triangle and Arrow?
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MHB What is the distance of closest approach
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Graduate What Does the Book Say About the Eigenvalues of 3x3 Matrices?
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Undergrad Simple Generalized Eigenvalue problem
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Undergrad The Complete Solution to the matrix equation Ax = b
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MHB 412.00.1.12 are relatively prime for all n.
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Undergrad General Form of Fourth Rank Isotropic Tensor: A Scientific Inquiry
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Undergrad What is the proper matrix product?
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Undergrad Is there any matrix equivalent for the Clifford product?
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MHB Introduction to linear algebra
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Undergrad Question about the Galois correspondence
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MHB Calculating LCD and GCD of 2 Sets of Numbers
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Undergrad Theory of "fields" in the sense of fields in physics?
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Undergrad What do you know about the planar product of two vectors?
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Undergrad Finding All Automorphisms of Group
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High School System of linear equations: When are we guaranteed a unique solution?
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MHB How to determine the bases B and C
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High School Solutions to systems of equations
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MHB What Is the Upper Bound of Groups of Order in Finite Group Theory?
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MHB Small Matrix Norm & Spectral Radius: Examples & Solutions
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MHB Show that the subspace U is ϕ^z-invariant
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MHB Proving or disproving this matrix V is invertible.
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MHB How to Translate Univariate Newton's Approximation to Multidimensional Systems?
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MHB Eigenspace is a subspace of V - ψ is diagonalizable
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Undergrad Irreducible representations of the Dn group
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Undergrad Matrices Commuting with Matrix Exponential
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High School Vector Notation: Italic Boldface Symbolization
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Undergrad Dot product in Euclidean Space
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MHB Relations between map and matrix
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MHB How Do Polynomial Functions Transform When Applied to Matrices?
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High School Do column 'vectors' need a basis?
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MHB Show that these elements are linearly independent
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MHB What is the spectrum of φ - Eigenspace in finite fields?
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MHB Show that φ(v)=λv for a vector v and a coefficient λ
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Undergrad Invertible Matrix Proof: A-Transpose * M * A (n by m)
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MHB Proving the Formula for Determinants by Induction
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High School How Is the Gradient Covariant in Different Coordinate Systems?
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Undergrad Need help with tensors and group theory
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Undergrad Determining the Equation of a Sine and Cosine Graph that speeds up
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Undergrad Proving Lorentz Transformation identities
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MHB Prove that the statements are equivalent
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Undergrad Understanding Lorentz Groups and some key subgroups
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MHB Proving Z[x] and Q[x] is not isomorphic
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MHB How to prove an ideal of a ring R which is defined as a coordinates
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Undergrad What criteria identifies a math operation as a "product"?
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Undergrad Explanation of a Line of a proof in Axler Linear Algebra Done Right 3r
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MHB Number of multiplications and divisions for LU decomposition
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MHB Understanding One-Sided Ideals in Mathematics
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MHB Statements with linearly independent vectors
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High School What are matrix transformations?
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Undergrad This linear system has a solution? (Gauss' elimination)
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MHB 311.1.4.6 create a vector equation
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MHB Creating Linearly Dependent Square Matrix from Cam Mechanism Equation
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Undergrad Rotate Functions with Derivatives: A Quantum Mechanics Homework
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MHB Complete augmented by row operations
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MHB What is the next step in Gauss-Jordan Elimination for this augmented matrix?
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MHB Such a decomposition exists iff A is positive definite
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MHB What is the Meaning of Operation gx in Group Theory?
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MHB Orthonormal basis - Set of all isometries
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Undergrad Spherical Harmonics Expansion convergence
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MHB Group mono-, endo-, iso-, homomorphism
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MHB Orthogonal Complement of Polynomial Subspace?
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MHB Is the composition of the isometries a rotation?
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MHB Subsets of permutation group: Properties
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MHB Understanding Vectors: Properties and Applications
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Undergrad Linear Subspace with Neutral Element in Brazilian Portuguese and Spanish
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Undergrad How to solve a small system of non-linear equations?
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Undergrad Building a coefficient matrix for a system of equations
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MHB How do unit vectors and eigenvalues relate to matrix A?
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MHB Test for compatibility of equations - Determinant |A b|
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MHB Show that there are vectors to get a basis
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MHB Kernel of Linear Map: Show $\ker \phi$ Equation
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Undergrad Proving Convexity of the Set X = {(x, y) E R^2; ax + by <= c} in R^2
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Undergrad The Paradox of u=v | Solve the Mystery
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MHB Is $2 + 8\sqrt{-5}$ a Unit or Irreducible in $\mathbb{Z} + \mathbb{Z}\sqrt{-5}$?
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Undergrad Logarithmic terms in a system of equations
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Undergrad Given two linear transformations L and K, show ##K = \lambda L## holds
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Undergrad Find the parameter values that make ##L## surjective
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MHB Method of least square: initial position & velocity
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MHB Projection Matrix Calculation for Vectors a_k: P_6P_5P_4P_3P_2P_1a_0
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MHB System no/infinitely many solution(s)
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MHB Is A Identical if A is a Square Matrix with Full Rank?
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MHB Prove that CnXCm isomorphic to Cgcd(m,n)XClcm(m,n)
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High School Rotating a point in 3-space through an angle about some vector
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Graduate Algebraic proof that Euler angles define a proper rotation matrix
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MHB Find Matrix A for System Ax=1, 3
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Graduate How do you invert a 3D matrix? (Tensor inversion)
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MHB Is the Condition Number of A'A Related to its Matrix Norm?
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Undergrad Is G simple?Is G simple? A different approach using Sylow theorems
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