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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Finding prize amounts for scientists and mathematicians
- Jodygreen
- · Replies 2 ·
Graduate For every positive integer n there is a unique cyclic group of order n
- BomboshMan
- · Replies 6 ·
Graduate Unifying Different Definitions of Adjoint Map
- WWGD
- · Replies 7 ·
Finding the projection of a vector.
- Jundoe
- · Replies 4 ·
How to Use Euclidean Division in $\mathbb{Z}_7$?
- evinda
- · Replies 2 ·
Undergrad Vector equations, possible to solve for x?
- Jonsson
- · Replies 8 ·
Why is sin(3pi/2) not equal to 1?
- nacho-man
- · Replies 10 ·
Graduate Component is diagonal in the basis
- vredina97
- · Replies 2 ·
Graduate Does Preimage of Subgroup Under Homomorphism Form a Subgroup?
- xiavatar
- · Replies 3 ·
Graduate Is it possible to solve for y using non-linear methods?
- pjoseph98
- · Replies 2 ·
Prove exactness of a sequence given exactness at all localizations at maximal ideals
- Fermat1
- · Replies 12 ·
Graduate Embedding Group as a Normal Subgroup
- WWGD
- · Replies 1 ·
Undergrad Are the Right and Left Cosets Equal in a Group's Cayley Table?
- mathsdespair
- · Replies 5 ·
Undergrad How can I use linear programming to distribute S into two bins?
- timeone
- · Replies 3 ·
Graduate Preliminary knowledge on tensor analysis
- ChrisVer
- · Replies 5 ·
Can This System of Equations Be Solved for Variables x, y, z, and Any?
- mrk79blr
- · Replies 5 ·
Undergrad Non-Symmetric Matrix: Real Eigenvalues Examples
- LagrangeEuler
- · Replies 1 ·
Graduate Confusion about basis vectors and matrix tensor
- nomadreid
- · Replies 2 ·
Graduate Equality involving matrix exponentials / Lie group representations
- MisterX
- · Replies 3 ·
Undergrad Matrix and transformation problem
- adjacent
- · Replies 4 ·
Undergrad Why are matrices used for stress and strain analysis?
- Tyrion101
- · Replies 4 ·
Graduate Is Tr(ABAB) Nonnegative for Symmetric Matrices A and B?
- jostpuur
- · Replies 8 ·
Undergrad Does Universal Algebra Have Applications in Physics?
- tmbrwlf730
- · Replies 2 ·
Graduate Interesting Subspaces of ##L^p## Spaces
- nateHI
- · Replies 14 ·
Graduate Are fractional polynomials linearly independent?
- dipole
- · Replies 1 ·
Graduate Matrix notation for Lorentz transformations
- decerto
- · Replies 1 ·
Undergrad Perpendicular force from cross product
- Miraj Kayastha
- · Replies 4 ·
Proving equivalence relations on specific sets
- the rambler
- · Replies 4 ·
Solve for D in ABDB⁻¹ = I with invertible NxN matrices
- das1
- · Replies 7 ·
Undergrad General expanded form of (x+y+z)^k
- sludger13
- · Replies 2 ·
Graduate Can Discriminants of Polynomial Equations Be Expressed Using Matrix Operations?
- Jhenrique
- · Replies 4 ·
Graduate Understanding Skew Symmetric Matrices for Physics - A Helpful Guide
- kq6up
- · Replies 7 ·
Greatest common divisor of polynomials
- evinda
- · Replies 3 ·
Looking for an Example of an Amusing Theorem in Linear Algebra.
- caffeinemachine
- · Replies 5 ·
Undergrad Inverse matrix notation question
- SamanthaYellow
- · Replies 3 ·
Graduate Position vector in curvilinear coordinates
- Jhenrique
- · Replies 2 ·
Undergrad What is the practical application of the trace of a square matrix?
- emergentecon
- · Replies 5 ·
Graduate Lie-algebra representation powers - plethysms
- lpetrich
- · Replies 40 ·
Graduate Compute the Quotient: [Z+Z]/[2Z+2Z]
- WWGD
- · Replies 2 ·
Undergrad Understanding Vector Transformations: Problem 1
- jellicorse
- · Replies 2 ·
Undergrad Why does (a.b).c make no sense?
- uzman1243
- · Replies 8 ·
How can you simplify generated ideals in a commutative unital ring?
- Fermat1
- · Replies 4 ·
How do right and left cosets differ?
- onie mti
- · Replies 4 ·
Graduate Proof of the Lindemann-Weierstrass Theorem
- smize
- · Replies 1 ·
Integral Ring Theory: Proving Integral Extension Property for Quotient Rings
- Fermat1
- · Replies 5 ·
High School Vectors - dot product and cross product?
- onceinalifetim
- · Replies 2 ·
Graduate Rotation of Gridded Spherical Coordinates to the Same Grid
- antennaist
- · Replies 3 ·
Graduate Proof of the nontrivial expression
- sludger13
- · Replies 7 ·
Undergrad What are Eigenvectors and Eigenvalues in Relation to Matrices?
- Jhenrique
- · Replies 1 ·
Undergrad Can a dot product be negative in case of length?
- EmSeeSquared
- · Replies 2 ·
Graduate What are universal properties all about?
- V0ODO0CH1LD
- · Replies 16 ·
Are \( x-a \) and \( x-b \) Co-primes?
- evinda
- · Replies 10 ·
Undergrad Where do the coefficients in this vector equation come from?
- mathsdespair
- · Replies 2 ·
Graduate How to derive det(I + A) ≈ 1 + Tr(A) for infinitesimal A
- spookyfish
- · Replies 2 ·
Why do we conclude that p|exactly one of b0,c0?
- evinda
- · Replies 3 ·
Undergrad Showing that V is a direct sum of two subspaces
- Seydlitz
- · Replies 6 ·
Undergrad Can I simplify (AB)(B⁻¹C) to AC?
- catsarebad
- · Replies 4 ·
Undergrad Can any vector be in orthonormal basis?
- catsarebad
- · Replies 6 ·
Undergrad How Does Cramer's Rule Relate to Geometry?
- member 428835
- · Replies 3 ·
Graduate How to prove if a recursive system is linear?
- Bipolarity
- · Replies 12 ·
Are all subrings and units correctly identified in algebraic structures?
- evinda
- · Replies 20 ·
Graduate Is the inverse of g_ab equal to g^ba?
- gentsagree
- · Replies 3 ·
Undergrad Identifying Largest Submatrices in a 0/1 Matrix?
- pablrodr
- · Replies 1 ·
Graduate Generalised eigenspace contains the eigenspace?
- Silversonic
- · Replies 2 ·
Find the coefficient of x^{21} without calculating the product
- mathmari
- · Replies 4 ·
Find all the zero divisors in a ring
- evinda
- · Replies 3 ·
Finding the Units of the Ring $R=\mathbb{Z}[w]$
- evinda
- · Replies 7 ·
Undergrad Is it Necessary to Keep Zero Columns in an Augmented Matrix?
- pondzo
- · Replies 6 ·
Do I Have to Show All Axioms to Prove a Set is a Ring?
- evinda
- · Replies 2 ·
Graduate Solving tridiagonal matrices with off-diagonal fringes efficiently
- maka89
- · Replies 1 ·
Why must the columns of a 3x5 matrix be linearly dependent?
- annie122
- · Replies 1 ·
P divides all the coefficients of the terms with degree <8
- mathmari
- · Replies 4 ·
Graduate What is the General Expression for the Product of Two Matrix Exponentials?
- dipole
- · Replies 1 ·
Undergrad Is "Multiplication Commutative in Rings?
- 1MileCrash
- · Replies 5 ·
Constructing a matrix version of the transformation algorithm?
- eleventhxhour
- · Replies 8 ·
Undergrad Why is the eigenvector for eigenvalue -6 equal to [0 0 1]?
- sozener1
- · Replies 3 ·
Graduate Solve wedge product of k vectors in (k+1)-dimensional space
- dimension10
- · Replies 13 ·
Undergrad Singular value decomposition and eigenvalue problem:
- maajdl
- · Replies 1 ·
Graduate Proof that symmetric matrices have eigenvectors without eigenvalues
- Seydlitz
- · Replies 6 ·
Graduate What is a Collineation and How Does it Differ from an Affine Transformation?
- cristina89
- · Replies 1 ·
Is $\Bbb Z_2 \times \Bbb Z_2$ a cyclic group?
- onie mti
- · Replies 6 ·
Undergrad Multiplication/division of matrices and vectors
- Jhenrique
- · Replies 6 ·
Undergrad Non-zero solution of a homogenous system
- sunny110
- · Replies 2 ·
Undergrad What is the geometric interpretation of the vector triple product?
- echandler
- · Replies 2 ·
Proving Even # of Transpositions for Identical Permutations
- simo1
- · Replies 1 ·
Partitions and equivalence relations
- simo1
- · Replies 1 ·
Optimal approximation and unique representation in Euclidean spaces
- mathmari
- · Replies 4 ·
What are Cyclic Subgroup Generators and How Do We Determine Them?
- onie mti
- · Replies 1 ·
Undergrad Questing about eigenvector order
- 939
- · Replies 2 ·
Graduate What is the Tensor Product and its Properties in Different States?
- Hluf
- · Replies 1 ·
Linear Equations - Cost per Pound of Coffee Beans
- AROJ
- · Replies 3 ·
Invertible matrices and encryption
- Minecrazy
- · Replies 2 ·
Undergrad Is the Cross Product Cancellative?
- Jhenrique
- · Replies 5 ·
What Is the Annihilator of a Quotient Ring?
- Sudharaka
- · Replies 2 ·
Graduate Can Hexagonal Sampling Improve Efficiency of Kronecker Product Matrices?
- 4real4sure
- · Replies 1 ·
Undergrad How Do You Write the Trace of AB* as a Summation?
- catsarebad
- · Replies 2 ·
Graduate Mathematics of circular shifts of rows and columns of a matrix
- pratchit
- · Replies 2 ·
Finding Units in $\mathbb{Z}[i]$: Is There More Than $1, -1, i$, and $-i$?
- evinda
- · Replies 5 ·
Square Matrix Proof: Diagonal Entries & Properties
- nacho-man
- · Replies 6 ·
How Do We Prove That 'P' Doesn't Vary for Different Free Variables?
- mathworker
- · Replies 1 ·