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.
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Characteristic Equations and Commutativity
- A.Magnus
- · Replies 7 ·
Undergrad Why does cA = A imply c is invertible in a simple unital ring?
- Math Amateur
- · Replies 2 ·
Undergrad Why scalar multiples of unity belong to the center of an algebra
- Math Amateur
- · Replies 17 ·
Why scalar multiples of unity are in the centre of an algebra
- Math Amateur
- · Replies 7 ·
Graduate Modular forms, dimension and basis confusion, weight mod 1
- binbagsss
- · Replies 12 ·
How Do I Find the Eigenvalues of \(F^2\) for the Derivative Mapping in \(X\)?
- A.Magnus
- · Replies 7 ·
Eigenvalues of 4x4 matrix with 3 on diagonal and -1 elsewhere
- A.Magnus
- · Replies 8 ·
Does gh = h'g for all h imply gH = Hg?
- alexmahone
- · Replies 4 ·
Undergrad Why does [D, L] = I in the first Weyl algebra A_1?
- Math Amateur
- · Replies 4 ·
Why does [D, L] = I in the first Weyl algebra A_1?
- Math Amateur
- · Replies 2 ·
Bresar Example 1.10: why does d E_il for all d in D imply I = M_n(D)?
- Math Amateur
- · Replies 1 ·
Undergrad Introduction to Simple Matrix Rings in Noncommutative Algebra
- Math Amateur
- · Replies 1 ·
Undergrad N-Dimensional Real Division Algebras
- Math Amateur
- · Replies 6 ·
How should this matrix be multiplied
- mathlearn
- · Replies 4 ·
Subgroups of the dihedral group D6
- mathmari
- · Replies 9 ·
Proving Determinant of Mirror-Image Identity Matrix
- A.Magnus
- · Replies 4 ·
How can we compute the Galois group of a subgroup of a splitting field?
- mathmari
- · Replies 1 ·
Undergrad Frobenius theorem proof in Bresar's noncommutative algebra book
- Math Amateur
- · Replies 6 ·
Undergrad Validity of proof of Cauchy-Schwarz inequality
- HaniZaheer
- · Replies 2 ·
Inverse of a 7×7 permutation matrix
- A.Magnus
- · Replies 7 ·
Permutation question concerning cycle shapes
- Confusedalways
- · Replies 1 ·
Frobenius theorem proof in Bresar section 1.4
- Math Amateur
- · Replies 2 ·
Finding 3 natural numbers by the rule of Sarrus
- A.Magnus
- · Replies 2 ·
Undergrad Proof of ij = -ji = k in Bresar's Lemma 1.3
- Math Amateur
- · Replies 3 ·
Undergrad Bresar Lemma 1.2: linear independence and membership in V
- Math Amateur
- · Replies 9 ·
Undergrad Do matrices with the same characteristic polynomial have the same trace?
- MrsM
- · Replies 11 ·
Undergrad Lemma 1.1 proof in Bresar's finite dimensional division algebras
- Math Amateur
- · Replies 14 ·
Show that the set of the upper triangular matrices is a ring
- mathmari
- · Replies 14 ·
Linear dependence implies minimal polynomial in Bresar Lemma 1.1
- Math Amateur
- · Replies 2 ·
Undergrad Finite Dimensional Division Algebras - Bresar Lemma 1.1
- Math Amateur
- · Replies 4 ·
Undergrad Does the first Sylow theorem imply groups of order p^k are cyclic?
- Silviu
- · Replies 1 ·
Determining when a system of equations has no solution and infinite solutions
- Ankit2
- · Replies 2 ·
Undergrad A regular matrix <=> mA isomorphism
- member 587159
- · Replies 11 ·
Undergrad Unitary Matrix Representation for SU(2) Group: Derivation and Verification
- spaghetti3451
- · Replies 3 ·
Graduate Differentiating a loss function L=wE where E=(G-Gest)^2 and G=F'F
- emmasaunders12
- · Replies 4 ·
High School Is identity matrix basis dependent?
- zonde
- · Replies 11 ·
The extension is Galois iff E is a splitting field of a separable polynomial of F[x]
- mathmari
- · Replies 1 ·
Undergrad Identifying the symbol at the end of this inertia tensor proof
- sa1988
- · Replies 6 ·
Showing A = I_m - X(X^TX)^-1X^T is idempotent
- mathmari
- · Replies 2 ·
How Do You Calculate Ore Production and Costs for Zinc and Aluminium?
- mathmari
- · Replies 12 ·
Index of Positivity in Quadratic Form: $f(X) = \sum^{n}_{i=1} x_{2}^{i}$
- A.Magnus
- · Replies 2 ·
Is there a more efficient way to determine the basis of a subspace?
- mathmari
- · Replies 2 ·
Dimension of Dirac Functionals in $V$: Find the Answer
- A.Magnus
- · Replies 8 ·
Graduate Quaternions: Extension of Real Numbers?
- Topolfractal
- · Replies 6 ·
The extension is Galois iff H_i is a normal subgroup of H_{i-1}
- mathmari
- · Replies 1 ·
Can the vectors be written as a linear combination?
- mathmari
- · Replies 5 ·
Undergrad From Non Hermitian to Hermitian Matrix
- IWantToLearn
- · Replies 2 ·
How Does Eisenstein's Criterion Confirm the Irreducibility of a Polynomial?
- mathmari
- · Replies 13 ·
Graduate (sum to infinity of divisor function)^{2} -- simplify the expression
- binbagsss
- · Replies 2 ·
Solve Exponential Fraction Equation for $α$ ($C$, $m$)
- Stijn
- · Replies 2 ·
Graduate Modular Forms: Non-holomorphic Eisenstein Series E2 identity
- binbagsss
- · Replies 1 ·
Show that the mapping is surjective
- mathmari
- · Replies 2 ·
How to Prove Galois Extension Statements in a Normal and Separable Field?
- mathmari
- · Replies 4 ·
How Can We Geometrically Describe Vectors Orthogonal to the Vector $(-4,1,-3)$?
- mathmari
- · Replies 2 ·
High School Why does <a|A†a|b> = <A†a|b>?
- Mayan Fung
- · Replies 8 ·
Undergrad Representing vectors with respect to a basis
- Mr Davis 97
- · Replies 8 ·
Undergrad How do you compute a rotation matrix around a given vector?
- Silviu
- · Replies 4 ·
Are Mutually Perpendicular Vectors Always Linearly Independent?
- A.Magnus
- · Replies 6 ·
Undergrad Why Is the Ratio of y2/y1 Not Constant for Linearly Independent Vectors?
- Cantspel
- · Replies 3 ·
Undergrad Linear regression on data collection error
- Travis T
- · Replies 2 ·
Undergrad Orthogonal basis to find projection onto a subspace
- Mr Davis 97
- · Replies 5 ·
Is Each Extension of Degree 2 Normal?
- mathmari
- · Replies 1 ·
Undergrad Normalizer of a subgroup of prime index
- Silviu
- · Replies 6 ·
Undergrad Intersection of quotient modules in Bland 4.2.4
- Math Amateur
- · Replies 3 ·
How can I prove the rank of a matrix with a specific pattern of entries?
- A.Magnus
- · Replies 2 ·
High School How do we obtain a Taylor expansion of a non-linear functional?
- naima
- · Replies 3 ·
Undergrad Why is the matrix ring (ℚ ℝ; 0 ℝ) right Artinian but not left Artinian?
- Math Amateur
- · Replies 2 ·
Right Artinian but not left Artinian matrix ring over Q and R
- Math Amateur
- · Replies 2 ·
Undergrad What is the meaning of N(H) in subgroup notation?
- Silviu
- · Replies 1 ·
Proving Positive Definite Scalar Product for $n \times n$ Matrices
- rputra
- · Replies 1 ·
Undergrad Solving simultaneous equations with matrix
- saranga
- · Replies 9 ·
Example from Bland - Right Noetherian but not Left Noetherian
- Math Amateur
- · Replies 5 ·
Undergrad Example - Bland - Right Noetherian but not Left Noetherian
- Math Amateur
- · Replies 9 ·
Undergrad Eigenvectors for degenerate eigenvalues
- dyn
- · Replies 7 ·
Question for null space of a matrix
- shiecldk
- · Replies 1 ·
Undergrad Free right R-module on X equals R^Λ in B&K section 2.1.16
- Math Amateur
- · Replies 2 ·
The irreducible polynomial is not separable
- mathmari
- · Replies 1 ·
Why Are My Gram-Schmidt Results Different on Wolfram|Alpha and MATLAB?
- nedf
- · Replies 3 ·
Undergrad Factorization of a matrix equation
- Mr Davis 97
- · Replies 6 ·
Undergrad Is the set {e^x, x^2} linearly independent?
- member 587159
- · Replies 4 ·
Finding a 3rd polynomial to create a basis.
- Harambe1
- · Replies 1 ·
Undergrad How to prove that shear transform is similarity-invariant?
- swampwiz
- · Replies 5 ·
Splitting Field of $g$ over $F$?
- mathmari
- · Replies 16 ·
Graduate 3dim Poincare Algebra - isl(2,R)
- bob2
- · Replies 5 ·
Undergrad Motivation and proof behind cross products
- Terrell
- · Replies 5 ·
Undergrad The Relationship Between Rank and Elements in a Jacobian Matrix
- spaghetti3451
- · Replies 2 ·
Undergrad What does adjacent indices mean in the context of matrix multiplication?
- Oppie
- · Replies 2 ·
Finding B^-1 in 3x3 Matrices with Linear Algebra
- mahmoud shaaban
- · Replies 3 ·
Graduate How Do Engel and Lie Arise Naturally?
- bolbteppa
- · Replies 5 ·
What does C^n over R mean for a vector space?
- karseme
- · Replies 3 ·
Undergrad What does ℝm×n mean for matrices and vectors?
- dyn
- · Replies 12 ·
Undergrad Ring homomorphism from the zero ring to R
- Math Amateur
- · Replies 10 ·
Undergrad Is Every Isomorphism in Vector Spaces Reflexive?
- member 587159
- · Replies 15 ·
Proving Convexity: Steps and Conditions for a Set to be Convex
- rputra
- · Replies 6 ·
Undergrad Are There n!/2 Even/Odd Permutation Matrices for nxn?
- Terrell
- · Replies 3 ·
Basic Question on Ring Homomorphisms
- Math Amateur
- · Replies 1 ·
Undergrad Proving Matrix exponential property
- kidsasd987
- · Replies 1 ·
The splitting field of f over F is also the splitting field of f also over E
- mathmari
- · Replies 1 ·
Zero matrix with non-zero above diagonal
- rputra
- · Replies 4 ·
Undergrad What does r^t a r = 1 mean in Raman spectra?
- chobo
- · Replies 4 ·