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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Undergrad How Do Elementary Operations Affect Matrix Rank Preservation?
- swampwiz
- · Replies 4 ·
High School Matrix A^(m+1) is different from A^(1+m)?
- Aldnoahz
- · Replies 2 ·
Undergrad Existence of basis for P_2 with no polynomial of degree 1
- Mr Davis 97
- · Replies 13 ·
Noetherian Modules and Submodules - J A Beachy, Proposition 2.4.5 .... ....
- Math Amateur
- · Replies 4 ·
Graduate Algebra - Clifford, Dirac, Lorentz
- spaghetti3451
- · Replies 1 ·
Graduate How Do Ladder Operators Annihilate States in SU(2) Algebra?
- spaghetti3451
- · Replies 6 ·
Is this a valid proof for the invertibility of $\Phi$?
- rputra
- · Replies 5 ·
Undergrad Proof that every basis has the same cardinality
- member 587159
- · Replies 2 ·
Undergrad Nonempty Subspace: Proving 0u = 0
- Mr Davis 97
- · Replies 2 ·
Show That $F(S)$ Is the Smallest Subfield of $K$
- mathmari
- · Replies 4 ·
Show that Q[π] is not a subset of Q(π)
- mathmari
- · Replies 8 ·
Undergrad Questions about linear transformations
- Mayan Fung
- · Replies 10 ·
Undergrad Understanding rectangular matrices
- Urmi Roy
- · Replies 7 ·
Finding the Matrix Associated with a Linear Mapping on a Real Matrix
- rputra
- · Replies 9 ·
Graduate Question on Cauchy-Schwarz inequality
- mnb96
- · Replies 8 ·
Find Group $G$ with Infinite Order Element: Ablien Not Allowed
- alexmahone
- · Replies 8 ·
Proving Divisibility of Polynomials in Field Extensions
- mathmari
- · Replies 2 ·
Undergrad Finitely Generated Modules .... another question
- Math Amateur
- · Replies 5 ·
Undergrad Finitely Generated Modules and Their Submodules ....
- Math Amateur
- · Replies 13 ·
Undergrad Vector Functions: v(r) Explained
- xoxomae
- · Replies 1 ·
Determinant of matrix with Aij = min(i, j)
- nedf
- · Replies 3 ·
Finitely Generated Modules and Their Submodules .... Berrick and Keating ....
- Math Amateur
- · Replies 2 ·
Undergrad Components of functions in vector spaces
- DoobleD
- · Replies 10 ·
Graduate For finite dimension vector spaces, all norms are equivalent
- ShayanJ
- · Replies 7 ·
High School Matrices concept confusion....
- Clara Chung
- · Replies 1 ·
I=<f> is maximal iff f is irreducible
- mathmari
- · Replies 12 ·
Proving Convex Set Properties to Showing the Convexity of X-Y
- rputra
- · Replies 3 ·
Undergrad I don't quite understand what i read
- Terrell
- · Replies 8 ·
Please, help with system of equations
- Nikolas7
- · Replies 2 ·
How can the convexity of a disk be proved using linear algebra?
- rputra
- · Replies 4 ·
Undergrad Finitely Generated Ideals and Noetherian Rings
- Math Amateur
- · Replies 7 ·
Finite Extension Simple iff Purely Inseparable Closure Simple
- caffeinemachine
- · Replies 1 ·
Show That F[u]=F(u): Proving with Theorem
- mathmari
- · Replies 2 ·
Finitely Generated Ideals and Noetherian Rings
- Math Amateur
- · Replies 2 ·
Undergrad Triangular Matrix RIngs .... Lam, Proposition 1.17
- Math Amateur
- · Replies 8 ·
Undergrad How Do You Prove a Matrix Ring is Right Artinian But Not Left Artinian?
- Math Amateur
- · Replies 8 ·
Undergrad Quick question about Lagrange's theorem
- TeethWhitener
- · Replies 2 ·
Undergrad Linear least-squares method and row multiplication of matrix
- Mesud1
- · Replies 2 ·
Proving disjoint of Kernel and Image of a linear mapping
- rputra
- · Replies 2 ·
How Do You Prove a Mapping is Surjective?
- rputra
- · Replies 3 ·
Triangular Matrix RIngs .... Lam, Proposition 1.17
- Math Amateur
- · Replies 1 ·
Undergrad Triangular Matrix RIngs .... Another Question
- Math Amateur
- · Replies 3 ·
Triangular Matrix Rings .... Another Question
- Math Amateur
- · Replies 1 ·
Is G an Abelian Group Given Specific Conditions?
- alexmahone
- · Replies 5 ·
Undergrad Why do eigenvectors stay the same when a matrix is squared?
- Aldnoahz
- · Replies 4 ·
Undergrad Concrete Examples of Exact Sequences in Linear Algebra
- andrew s 1905
- · Replies 13 ·
What are the ideals of the matrix ring?
- Math Amateur
- · Replies 6 ·
Maximal Ideals - Exercise 5.1 (ii) Rotman AMA
- Math Amateur
- · Replies 6 ·
Example on Triangular Rings - Lam, Example 1.14
- Math Amateur
- · Replies 4 ·
Undergrad Example on Triangular Rings - Lam, Example 1.14
- Math Amateur
- · Replies 2 ·
Undergrad Points of a finite projective line
- Lapidus
- · Replies 1 ·
Approaching Question C1: Finding Roots of Elements in a Field
- Kiwi1
- · Replies 4 ·
High School How do we know if something is vector or scalar quantity?
- Faiq
- · Replies 6 ·
Undergrad Expanding linear independent vectors
- member 428835
- · Replies 2 ·
Undergrad Understanding Subspaces: Definition and Examples | PF Study Guide
- member 428835
- · Replies 3 ·
Undergrad How to Construct an Orthonormal Basis for a 2D Subspace in Linear Algebra?
- vibe3
- · Replies 3 ·
Graduate Expectation operation for covariance calculation
- nikozm
- · Replies 1 ·
Undergrad Coordinate transformation of a vector of magnitude zero
- Battlemage!
- · Replies 3 ·
Undergrad Fundamental Theorem of Arithmetic - Bhattacharya et al
- Math Amateur
- · Replies 5 ·
Fundamental Theorem of Arithmetic - Bhattacharya et al - Ch. 2, Section 1
- Math Amateur
- · Replies 4 ·
Maximal Ideals - Exercise 5.1 (iii) Rotman AMA
- Math Amateur
- · Replies 3 ·
Undergrad Are the columns space and row space same for idempotent matrix?
- arpon
- · Replies 6 ·
A little problem on exact sequences, part 2.
- steenis
- · Replies 4 ·
Prime and Maximal Ideals in PIDs .... Rotman, AMA Theorem 5.12
- Math Amateur
- · Replies 3 ·
Undergrad Newton's formula for the sums of powers of roots?
- Clara Chung
- · Replies 2 ·
Prove Z7 is a Ring Under + and x Operations
- Zoey93
- · Replies 3 ·
Undergrad Prime and Maximal Ideals in PIDs ... Rotman, AMA Theorem 5.12
- Math Amateur
- · Replies 4 ·
How Does the Correspondence Theorem for Rings Prove Maximal Ideals?
- Math Amateur
- · Replies 3 ·
Undergrad Maximal Ideals and the Correspondence Theorem for Rings
- Math Amateur
- · Replies 3 ·
Normal Extensions and Normal Subgroups
- Kiwi1
- · Replies 1 ·
A little problem on exact sequences.
- steenis
- · Replies 7 ·
Undergrad Constructing a vector from a point
- Mr Davis 97
- · Replies 2 ·
Undergrad Transpose Property (where's my mistake)
- member 428835
- · Replies 3 ·
Undergrad A double in this example problem
- Muthumanimaran
- · Replies 3 ·
Undergrad Show that the diagonals are perpendicular using vectors
- Mr Davis 97
- · Replies 2 ·
High School Vector perpendicular to a plane defined by two vectors
- Mr Davis 97
- · Replies 5 ·
Vector in 3d with given by magnitude and angle
- cbarker1
- · Replies 1 ·
Undergrad Use Lorentz Force to Find Magnetic Field Components
- peasqueeze
- · Replies 6 ·
Undergrad Can RREF be used for any size matrix?
- Mr Davis 97
- · Replies 9 ·
Undergrad Matrix Component Equation: Solving for B with Known Scalar and Indices
- member 428835
- · Replies 4 ·
Undergrad Kronecker Delta summation (easy)
- member 428835
- · Replies 6 ·
High School The equation relating a vector to a unit vector
- Mr Davis 97
- · Replies 6 ·
Prove: \(F(a,b)^*=F(a) \cup F(b)\)
- Kiwi1
- · Replies 4 ·
Ice cream & yogurt matrices problem
- mathlearn
- · Replies 5 ·
Undergrad Two-sided Prinicipal Ideal - the Noncommutative Case - D&F
- Math Amateur
- · Replies 3 ·
Why Is the Set {ras | r, s ∈ R} Not a Two-Sided Ideal in Noncommutative Rings?
- Math Amateur
- · Replies 2 ·
Undergrad Understanding SU(2) Representations and Their Role in Particle Physics
- Silviu
- · Replies 2 ·
Undergrad Module Over a Division Ring - Blyth Theorem 1.1, Part 4
- Math Amateur
- · Replies 11 ·
Undergrad State of a Generator in Representation Theory
- Silviu
- · Replies 3 ·
High School Tensor Calculus vs Tensor Analysis?
- ibkev
- · Replies 2 ·
Undergrad What is the name of the matrix decomposition with specific properties?
- Ken Gallock
- · Replies 6 ·
Undergrad No problem, it's always good to have multiple sources!
- Silviu
- · Replies 6 ·
Finding the zero vector of a sinusoidal set
- Apricity
- · Replies 2 ·
Submodules A + B and A intersect B .... Blyth Ch. 2
- Math Amateur
- · Replies 3 ·
Undergrad Submodules A + B and A intersect B .... Blyth Ch. 2
- Math Amateur
- · Replies 2 ·
Theorem 2.3: Submodule Generation by Family of Submodules - T. S. Blyth
- Math Amateur
- · Replies 2 ·
Undergrad Submodule Generated by Family of Submodules -Simple Question
- Math Amateur
- · Replies 2 ·
High School Is the Inverse of this Matrix Possible?
- askor
- · Replies 12 ·
Undergrad Interpretation of direct product of Hilbert spaces
- IanBerkman
- · Replies 4 ·
Undergrad Coordinate System: Understanding Polar Vectors
- Devil Moo
- · Replies 8 ·