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 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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Graduate Mathematical term for physicist's "Lattice Theory"?
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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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MHB LU decomposition: With or without pivoting?
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Graduate 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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MHB Proving $x-1$ is a Factor of $P(x)$ with Polynomials
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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 Proving Orthogonal Projection of Triangle V, v'_{1}
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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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MHB Set is closed as for multiplication of matrices
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MHB B=Q^TAQ has a LU decomposition
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Undergrad Showing that a set of differentiable functions is a subspace of R
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MHB How to Choose the Right Running Shoes for You
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MHB Tips for Eating Healthy on a Budget
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MHB What is the form of that matrix?
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Undergrad P-adic valuation expression for a given natural number
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High School In algebra what does x represent?
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Graduate Algebra of divergent integrals
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Undergrad Definiteness of a nonsymmetric matrix
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MHB Proving Zp is a Vector Space for Prime p
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Undergrad Proving linear independence of two functions in a vector space
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Graduate Order of group, Order of element
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MHB For which c is there 1/0 solution?
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Undergrad How Are Dual Vectors and Covectors Related in Vector Spaces?
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MHB Linear system of equations: Echelon form/Solutions
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Undergrad The Value and Applications of Group Theory in Mathematics
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Undergrad Is there a theorem that a set of binary swaps can affect any permutation?
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MHB Calculating the Inverse Matrix for a 3x3 Matrix
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Undergrad Is Complex Differentiation Defined for Linear Transformations?
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MHB Solving System of Equations: xy, yz, zx
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Graduate How to investigate a transformation that might form a Lie group?
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MHB 311.1.5.12 Ax=0 in parametric vector form
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MHB Is G/G isomorphic to the trivial group? A proof for G/G\cong \{e\}
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Undergrad Decomposition per the Fundamental Theorem of Finite Abelian Groups
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Graduate Finite non-abelian group of the order pq, pq primes
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MHB -311.1.5.8 Ax=b in parametric vector form,
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MHB 311.1.5.5 homogeneous systems in parametric vector form.
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Undergrad Prove that dim(V⊗W)=(dim V)(dim W)
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Undergrad Hermitian Operators and Non-Orthogonal Bases: Exploring Infinite Spaces
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Undergrad Does anyone really understand what's really going on with this video?
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Undergrad What is the definition of trace for n-indexed tensor in group theory?
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Undergrad Rotational invariance of cross product matrix operator
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Undergrad Trying to get a better understanding of the quotient V/U in linear algebra
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Undergrad Understanding Algebraic Numbers & Proving Them
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Undergrad Why does A squared not equal A times A when k = Z2?
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Undergrad How to approach a cross product question
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Undergrad Three equations of planes, dimension should be 1?
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Undergrad Show that ##\mathbb{C}## can be obtained as 2 × 2 matrices
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MHB Connecting linear algebra concepts to groups
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MHB Resource for learning linear algebra
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