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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.
Undergrad Proof that if T is Hermitian, eigenvectors form an orthonormal basis
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MHB What is the GCD and LCM of 35280 and 4158?
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MHB Invariance of Asymmetry under Orthogonal Transformation
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Graduate Vectors as geometric objects and vectors as any mathematical objects
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MHB Is Every Group of Order 25 Cyclic?
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MHB Could you prove that f(A)>=0 whenever A>0?
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Undergrad Linear independence of three vectors
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MHB *elements and generators of U(14)
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Graduate Solving algebraic equations that cannot be solved in radicals
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Undergrad Proof about a positive definite matrix
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Graduate Anti-dual numbers and what are their properties?
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Graduate Tensor product matrices order relation
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Undergrad Understanding zero divisors & ##\mathbb{Z_m}## in Ring Theory
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MHB How Do You Map Matrices to Complex Numbers in Linear Algebra?
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Graduate Eigenvalue of the sum of two non-orthogonal (in general) ket-bras
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Undergrad Matrix representation for closed-form expression for Fibonacci numbers
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Undergrad Different norms and how L1 leads to the sparsest solution
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Undergrad Prove the given properties - Ring Theory
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Undergrad Continued fractions and nested radicals
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Undergrad What is the difference between a complete basis and an overcomplete dictionary?
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Undergrad Is tensor product the same as dyadic product of two vectors?
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Undergrad What are the Eigenvalues of the Hermitian Inverse \(H^{-1}\)?
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MHB Proving Properties of 2x2 Matrices
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MHB Does Commutativity Hold for Matrices A and B with a Specific Matrix C?
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MHB Maxima and Minima (vector calculus)
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Undergrad Does Axler's Spectral Theorem Imply Normal Matrices?
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Undergrad A few questions about doing a Gaussian Fit
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Undergrad Determinant of a specific, symmetric Toeplitz matrix
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MHB An Overview of the History of Tea
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Undergrad How is uniqueness about the determinant proved by this theorem?
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High School Does this kind of square matrix exist?
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Undergrad Confused about dot product of a and b = |a||b| if theta = 0
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Undergrad Graph Representation Learning: Question about eigenvector of Laplacian
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Undergrad What Does the F Matrix Look Like for a Linear Bezier Curve?
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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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MHB 6.2.8 {{k,4},{3,k}}=k what is k
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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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Undergrad Factoring Matrices with Elementary Row Operations
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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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MHB How Do You Solve Linear Equations with Given Coordinates?
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Graduate What is the Definition and Properties of a Cross Product in Vector Algebra?
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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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MHB Solve System Using Matrix Inverse
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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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