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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.
Graduate First eigenvalue not matching, but all others are
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Undergrad This is an invalid argument about eigenvalues, but why?
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Undergrad Can integers be defined as N[[sqrt(1)]]?
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High School Inductive proof for multiplicative property of sdet
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Undergrad Manipulation of 2nd, 3rd & 4th order tensor using Index notation
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Undergrad The way matrices are written without boxes
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High School Inverse of a Vector: Find the Correct Form
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High School Is Super Commutativity Essential in Defining a Super Lie Module?
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Undergrad Proof that two linear forms kernels are equal
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High School Recurrence relation in a recurrence relation?
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Undergrad Contracted Christoffel symbols in terms determinant(?) of metric
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Undergrad Convert cylindrical coordinates to Cartesian
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High School One-to-many relations in group theory
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Undergrad What is the importance of p-Sylow subgroups in understanding group structure?
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Undergrad Generators of Galois group of ## X^n - \theta ##
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High School Determinant of a transposed matrix
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Graduate How Does the Non-Equality of Kernels Imply Their Sum Equals the Vector Space?
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Graduate Reason out the cross product (for the moment): a skew symmetric form
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Graduate Calculating the Modal Matrix for A
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Undergrad What Conditions Ensure the Minimal Polynomial of α Divides P in Galois Theory?
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Graduate How to visualise complex vector spaces of dimension 2 and above
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Undergrad Basis of 2x2 matrices with real entries
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Undergrad Proving properties of polynomial in K[x]
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MHB What Are the Possible Jordan Forms and Characteristic Polynomial of T?
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Undergrad How to find the generator of this Lie group?
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MHB Group Elements of Z24: Find the Order
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MHB Number of solutions for system of equations
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MHB -la.1.1.19 the augmented process
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Undergrad Orthogonality of Eigenvectors of Linear Operator and its Adjoint
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Undergrad Does associativity imply bijectivity in group operations?
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Graduate Need some clarifications on tensor calculus please
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MHB 3.13 Compute the orders of the following groups:
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MHB 307.8.1 Suppose Y_1 and Y_2 form a basis for a 2-dimensional vector space V
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MHB 307.8.3 Compute A^n for the Jordan block
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MHB 311.3.1.1 - Determinants And Cofactor Expansion
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MHB What are the generators of $\Bbb{Z}_6, \Bbb{Z}_8,$ and $\Bbb{Z}_{20}$?
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MHB Set of vectors form a vector space
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MHB Describes elements of D_5 using SAGE
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MHB Z6: Identity, Order, Inverse, Generator, Abelian/Non-Abelian, Subgroups
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Undergrad What Is a Dyadic? - Understanding What They Are & How To Use Them
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Undergrad Linear Algebra 1 problem, Vector Geometry: Lines
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Undergrad Is This a Valid Basis for the Set of Polynomials with \( p(0) = p(1) \)?
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Undergrad S is set of all vectors of form (x,y,z) such that x=y or x =z. Basis?
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High School Proof involving two linear equations
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Undergrad How can I find all possible Jordan forms?
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Undergrad Looking for a creative or quick method for finding roots in GF(p^n)
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Undergrad Similarity transformation, basis change and orthogonality
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Undergrad Irreducible polynomials and prime elements
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Graduate Matrix Multiplication: Solving A*A'=B for Unique A(B)
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Undergrad Anyone knows why musical isomorphism is called so?
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Undergrad Finding a polynomial that has solution (root) as the sum of roots
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Undergrad Proving the Existence of Roots in Complex Polynomials
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MHB Proof of Complex Numbers: Delta*w(z, z) Explained
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MHB Finding a Basis for a Linear Subspace Orthogonal to a Given Point P in R^3
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Undergrad Interesting Article Ref: Sudoku and Linear Algebraic aspects
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Undergrad How to Show U|v⟩ = e^(ia)|v⟩ for Unitary Operators?
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Undergrad Proving ##\partial^{i} = g^{ik} \partial_{k}##
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Undergrad Why are determinants in 2x2 matrices and 3x3 matrices computed the way they are?
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Undergrad Understanding the Results of gcd(x,n)
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Undergrad I think I've hit upon a very easy proof of impossibility of quintic
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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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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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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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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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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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