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 Matrix Transforms: nxm, n->m, m->n, n+m->n/m
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Undergrad The tensor product of tensors confusion
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High School Is it invalid to redefine the sgn function in this way in a proof?
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High School What Are Solutions for Universal Linear Recursions?
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Graduate Center of a linear algebraic group
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High School Proving the uniqueness of eigenspaces
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MHB QR decomposition with permutation matrix
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MHB Approximation of eigenvalue with inverse iteration method
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MHB Scalar Triple Product and Coplanarity
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MHB Householder method : Which α do we take?
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Undergrad Central Extension and Cohomology Groups
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Undergrad Prove that the limit of this matrix expression is 0
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High School Any square matrix can be expressed as the sum of anti/symmetric matrices
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High School Geometrical meaning of magnitude of vector product
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MHB Find Vector of Given Length in Particular Direction
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MHB What is the Angle Between Vectors Using the Dot Product Formula?
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MHB Find Vector Perpendicular to Plane
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Graduate Link between 24 dimension kissing number and Monster group
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Undergrad How to Find the Generalized Eigenvector in a Matrix ODE?
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MHB Abstract algebra: i need examples of ...
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MHB Proving Non-Degeneracy of Euclidean Inner Products
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Graduate A problem in multilinear algebra
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High School Regarding Contravarient Vector Transformations
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Undergrad Proving (x,x) = 0 implies x = 0 in real vector space V
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MHB Velocity and acceleration vectors and their magnitudes
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MHB Understanding Velocity and Acceleration of a Moving Particle
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Undergrad Shouldn't this definition of a metric include a square root?
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MHB How is Radius of Curvature Computed for a Given Curve?
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MHB Prove R is a Sub-ring of $\mathbb{Q}$ - Prime $p \in \mathbb{Z}$
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Undergrad Proving that ##V = U_1 \oplus U_2 \oplus \ldots \oplus U_k##
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Undergrad Understanding the concept of direct sum
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MHB Diagonalizable transformation - Existence of basis
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Undergrad Proving U_1 + U_2 + ... + U_k = span (U_1 \cup U_2 \cup \ ... \ \cup U_k)
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MHB Is the Matrix A Diagonalizable with Real Eigenvalues?
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High School Commutators of functions of operators
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MHB Is x+1 a Factor of the Polynomial x^3-5x^2+3x+1?
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Undergrad Meaning of terms in a direct sum decomposition of an algebra
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Graduate Lie Bracket * Matrix * vector (Need proof)
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MHB What is the velocity vector after a pinball bounces off a baffle?
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Undergrad How is unit norm axis rotation represented and derived in R3?
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Undergrad Dimension of a Linear Transformation Matrix
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MHB Is the Calculated Osculating Plane and Binormal Correct for $\theta=0$?
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MHB Prove $10^{\dfrac{5^n -1}{4}} \Huge\vert (5^n)!$ for $Z^+$
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Undergrad Canonical Form for quadratic equations *with* linear terms
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Undergrad Two ways to define operations in a vector space
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Undergrad Un-skewing a skew symmetric matrix (for want of a better phrase)
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High School Magnitudes of the sum of two vectors
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MHB Find the elementary divisors and invariant factors
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Undergrad How can the Lp Norm be used to prove inequalities?
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Undergrad Question about the vector cross product in spherical or cylindrical coordinates
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MHB The product γ is a rotation or a translation
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MHB What are the properties of affine bases in $\mathbb{R}^n$?
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MHB Checking if $\beta \in \text{Isom}(\mathbb{R}^2)$
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Graduate Multinomial functions of matrices
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MHB Set of 2-dimensional orthogonal matrices equal to an union of sets
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Graduate Trace of the inverse of matrix products
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Undergrad What conditions are needed to raise a linear operator to some power?
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Undergrad Commutative algebra and differential geometry
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High School Explicit expression for ideal membership
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MHB Hectares and kilometres - how many days to cut 295 hectares
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Undergrad One-Time Pad and Frequency Analysis
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MHB 3.2.5.3 General Solution if system
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MHB Solving 2nd-Order IVP as System of Equations
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Graduate Error in (Multi)linear Regression
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MHB Find Eigenvalues & Basis C2 Matrix: Help!
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Graduate Infinite-Dimensional Lie Algebra
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MHB System of Equations for Second-Order IVP
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MHB 097 Change the second-order IVP into a system of equations
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Undergrad Change of Basis Matrix vs Transformation matrix in the same basis....
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MHB Solving Matrix A: Characteristic Equation and Eigenvectors
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Undergrad Reducing NxN Matrix to 2x2 w/ Physical Constraints
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Undergrad Theory of Schemes in Algebraic Geometry
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MHB Λ and μ are scalars, find the value of λ and the value of μ
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Graduate How to Solve B^3 = A^2 Matrix 2x2 on C?
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Undergrad Determine if polynomial system has finite number of solutions
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Undergrad Help solving a System of Linear Equations
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Graduate Understanding of conjugate directions
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Undergrad Weird Semidirect Product Formula
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Undergrad Determining the number of conjugacy classes in a p-group
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MHB 5.2a plot linear transformations
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Undergrad Can a group be isomorphic to one of its quotients?
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High School Giving definitions, proposing theorems in abstract spaces
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MHB 072 is Q(theta) a linear transformation from R^2 to itself.
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Undergrad When is it better to call a thing "modulus" and when "determinant"?
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MHB T20 Suppose that A is a square matrix of size n and ......
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Graduate Translationlength by the coxeterelement of E9 along the coxeteraxis
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Undergrad Permutations written as product of 2-cycles
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MHB Matrices.......whose null space consists all linear combinations
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MHB Whit.a.6.1 Show that the plane H defined by:
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MHB 051 how they got the eigenspaces ?
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Undergrad The adjective "finite" applied to algebraic structures
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Undergrad General worked out solution for diagonalizing a 4x4 Hermitian matrix
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MHB Q01 are linearly independent vectors, so are....
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Graduate What physical meaning can the “determinant” of a divergency have?
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MHB Give a basis to get the specific matrix M
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MHB Equivalence of Subspace Statements
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MHB Row echelon form : Can the first column contain only zeros?
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Graduate What is the Corollary of the Nucleus and Image Theorem?
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MHB M has the unit matrix at the upper left side and zero everywhere else
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MHB Rank of composition of linear maps
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