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 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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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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Undergrad Reducing NxN Matrix to 2x2 w/ Physical Constraints
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Undergrad Theory of Schemes in Algebraic Geometry
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Graduate How to Solve B^3 = A^2 Matrix 2x2 on C?
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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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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 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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Graduate Eigenvalues of block matrix/Related non-linear eigenvalue problem
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MHB How Are the Vectors $z_1$, $z_2$, and $z_3$ Created in the Span?
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Undergrad What is the logarithm of the derivative operator?
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MHB T31 vector subtraction is not commutative and not associative.
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Undergrad Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix
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MHB Does Linear Independence in V Imply the Same in W?
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Undergrad How to Prove a Congruence Relation for Prime Numbers?
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Graduate Topology on a space of Lie algebras
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Undergrad Taylor expansion of an unknown function
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High School What is the cross product of two vectors?
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Undergrad Do These Vectors Span V?
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MHB If 2 columns are identical is there infinite solutions
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MHB Solving Systems of Six Equations with Nine Variables
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MHB 307w.WLCA.C10 computations are linear?
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Undergrad ##(p^k -1) \equiv X \mbox{(mod p)}## via Wilson's theorem
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MHB Construct 3 Augmented Matrices for Linear Systems
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MHB 307w.43.M40 find corresponding 3 scalars
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Undergrad Why doesn't sinc(x) converge to Gaussian upon repeated convolution?
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Graduate What is the difference between groups SU(n) and SO(n,C)?
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Undergrad Rodrigues' rotation formula from SO(3) comutator properties
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High School Orthogonal Projections: Same Thing or Not?
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Undergrad Solving a complex linear system with parameters
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Undergrad Domain of convolution vs. domain of Fourier transforms
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MHB 311.1.5.19 parametric equation of the line through a parallel to b.
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Graduate Understanding the Relationship between Orthogonal and Unitary Groups
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MHB Linearly Dependent Vectors: Find h Value and Justify
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Graduate Matrix multiplication, Orthogonal matrix, Independent parameters
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High School Graph of ax+by=c: How a,b,c Affects Graph
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Graduate Is the notion of elementary function a fluid concept among algebras?
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MHB 311.1.7.9 For what values of h is v_3 in Span {v_1,v_2,v_3}
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Undergrad Proof concerning the Four Fundamental Spaces
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MHB 311.1.5.14 Use vectors to describe this set as a line in R^4
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Undergrad If L is diagonalizable, algebraic & geometric multiplicities are equal
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Undergrad Understanding Unfaithful Representations of Z_2 in the Caley Table
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MHB 311.1.5.17 geometric description
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MHB Is b a linear combination of a1, a2, and a3?
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Undergrad Decomposing arbitrary representations
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Error in Sadri Hassani's Mathematical Physics
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High School A problem involving direction cosines (Vector Algebra)
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MHB 311.1.3.19 find h and k in the system
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MHB 311.3.2.16 Find the determinant with variables a b c d e f g h i
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Undergrad What is the Dimension of SO(3) with Constraint det(O) = 1?
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High School What is the identity element in the group {2,4,6,8} under multiplication mod 10?
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Undergrad Poincaré algebra and quotient group
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MHB 307.1.1 Use row reduction on the appropriate augmented
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Undergrad Group and Identity: Proving (12)(34)² = (12)(34)
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MHB 311.1.3.2 u+v and u-2v and tikx?
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Undergrad Invertible Polynomials: P2 (R) → P2 (R)
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Graduate How Do You Apply Noether Normalization to a Polynomial Ring Ideal?
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Undergrad Determine the limit in a Markov process over time
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MHB Symmetry Operations of a Cube: Geometric Descriptions and Matrix Representations
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MHB Subsets of $\mathbb{R}^2$ Satisfying S2 and S3 but Not S1: Empty Set
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MHB Solve Sets of Form $v+X$ in $\mathbb{R}^2$
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MHB 311.2.2.6 use inverse matrix to solve system of equations
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Undergrad Base Pi Integers: Isomorphism with Rationals?
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MHB Does the Cosine Rule Apply to Vector Addition in 3-D?
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