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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High School Finding Shortcuts to Solve Big Math Problems
- slug
- · Replies 8 ·
Graduate Is T an Isomorphism and How Can It Be Proven?
- laminatedevildoll
- · Replies 4 ·
Graduate Where to Find Original Manuscript of Proof of Taniyama Shimura Conjecture?
- Leopold Infeld
- · Replies 2 ·
High School What Do Digit Counts Mean in Prime Number Tables?
- endfx
- · Replies 44 ·
Graduate Why is A(n) an integer only for n = 1 and n = 24?
- AntonVrba
- · Replies 8 ·
Graduate Can we identify vector elements independent of basis choice?
- Kocur
- · Replies 10 ·
Graduate Question in regards to Permutation matrices, basis, and non linear functions
- SupaNerd
- · Replies 2 ·
Graduate Is f an Eigenfunction of Operator A Given the Equality <f|A f>² = <f|A² f>?
- TeCTeP
- · Replies 7 ·
Undergrad Why can't irrational numbers be expressed as ratios if rationals get arbitrarily close?
- Sunshine
- · Replies 9 ·
Graduate How to Find a Maximal Subset of X in V=C[0,1]?
- laminatedevildoll
- · Replies 2 ·
Graduate How can I calculate the Killing form of a Lie algebra using a specific basis?
- Dogtanian
- · Replies 5 ·
Graduate Is the Adjugate of a Singular Matrix Also Singular?
- loli12
- · Replies 5 ·
High School Why is zero so important in mathematics
- strid
- · Replies 112 ·
Graduate Vector Space P_4: Basis with Tchebychev Polynomials
- laminatedevildoll
- · Replies 8 ·
Graduate Physics book reference for SL(2,C) representations and generators
- dextercioby
- · Replies 20 ·
Graduate A VERY interesting Fermat-like sequence: A_n=4^3^n+2^3^n+1
- T.Rex
- · Replies 3 ·
Undergrad Triangle Inequality: True or False?
- blinder
- · Replies 2 ·
High School Can You Solve the Equation 5^n = 80n for n?
- One-D
- · Replies 5 ·
Graduate Reflection matrix for y=-4x and rotation about [1,2,2]
- laminatedevildoll
- · Replies 2 ·
Graduate Proving divisibility properties of Pell companion sequence V_n
- T.Rex
- · Replies 2 ·
Graduate Proving V+J=k[x] using induction for k with polynomial ring in n variables
- grimster
- · Replies 2 ·
Graduate Ordenation of the complex number and its consequences
- aviator
- · Replies 2 ·
Graduate Proving Independent Functions: Wronskian for n=2
- dogma
- · Replies 3 ·
Undergrad Which Math Course to Choose for a Physics Major: Algebra I or Linear Algebra I?
- singleton
- · Replies 8 ·
Graduate Can the Direct Sum of Cyclic Groups Determine the Properties of Finite Groups?
- Zaare
- · Replies 11 ·
Graduate Proofs in Linear Algebra: Countable Sets, Algebraic Numbers, and Fields
- blaster
- · Replies 2 ·
Undergrad Cross Product in R^n: Defined or Undefined?
- quasar987
- · Replies 7 ·
Undergrad Curves intersecting at the origin
- b0mb0nika
- · Replies 8 ·
Undergrad Motivations for eigenvalues/vectors
- eckiller
- · Replies 4 ·
Undergrad Does a singular n×n matrix always give infinitely many solutions?
- blinder
- · Replies 3 ·
Graduate Triangular numbers, T(An +B), that equal (Cn+D)*(En+F) for all n
- ramsey2879
- · Replies 3 ·
Graduate Nabla operator to geometric product
- Raparicio
- · Replies 2 ·
High School Applications of Linear Equations Monetary Word Problem
- dajohu
- · Replies 2 ·
Undergrad How can I prove the invertibility of a diagonalizable matrix?
- randommacuser
- · Replies 10 ·
Graduate Why is the zero element unique if cos(0) = cos(2π)?
- randommacuser
- · Replies 4 ·
Graduate Solutions to 2^n+1=m² with Pell and NSW numbers
- T.Rex
- · Replies 2 ·
Undergrad Finding x so matrices A and B have the same row space
- Cyannaca
- · Replies 4 ·
Graduate I name this number the Near Integer Ratio Rv
- AntonVrba
- · Replies 21 ·
Graduate Discussing the Near Step Function for γ=0.4823241136337762
- AntonVrba
- · Replies 5 ·
Graduate Proving Similar Matrices Have the Same Characteristic Polynomial
- EvLer
- · Replies 2 ·
Undergrad Finding k for Linear Dependence in a Vector Space
- Cyannaca
- · Replies 2 ·
Graduate Are Orthogonal Matrices Compact?
- blaster
- · Replies 2 ·
Graduate Yoneda lemma: natural transformation Hom(_, A) to Hom(_, B)
- Hurkyl
- · Replies 3 ·
High School Where Can I Find Resources for Learning About Matrices and Solving Methods?
- chandran
- · Replies 1 ·
Undergrad Matrix Multiplication: Can You Multiply a Matrix in the Middle?
- EvLer
- · Replies 2 ·
Undergrad Nullspace of non-zero 4x4 matrix
- EvLer
- · Replies 6 ·
Undergrad Are These Sets Vector Spaces?
- madking153
- · Replies 8 ·
Graduate Existence of n T-invariant Subspaces in Vector Spaces and Linear Operators
- graceytigger
- · Replies 2 ·
Graduate 2 non-zero matrix A and B, and A*B=0
- blaster
- · Replies 2 ·
Undergrad Linear (in)dependent vector sets
- madking153
- · Replies 3 ·
Undergrad Why Are Diagonalized Matrix Columns the Eigenvectors?
- toffee
- · Replies 3 ·
Undergrad Are non-orthogonal bases possible?
- EvLer
- · Replies 29 ·
Undergrad How Can We Determine the Value of p to Make Three Vectors Coplanar?
- Ryoukomaru
- · Replies 4 ·
Undergrad Simple example of a Markov chain
- nktvnvn
- · Replies 2 ·
Graduate Me, myself and conjugate permutations
- Chen
- · Replies 8 ·
Undergrad Expressing Natural Numbers as Sum of Primes
- metrictensor
- · Replies 13 ·
Graduate Prove that a set is a monoid, but not a ring.
- grimster
- · Replies 5 ·
Undergrad Algebra: Expressibility of f(x) with 10 Numbers
- sid_galt
- · Replies 6 ·
High School How can you rearrange a formula to make a specific number the subject?
- mtanti
- · Replies 2 ·
Graduate Determinat of a continous matrix?
- wenty
- · Replies 4 ·
Graduate Linear transformation, show surjection and ker=0.
- grimster
- · Replies 9 ·
Graduate Visualizing associative and distributive properties in rings
- BicycleTree
- · Replies 22 ·
Undergrad Patterns of Solution Sets of a System of Linear Equations
- e(ho0n3
- · Replies 2 ·
Graduate General Definition of Relatively prime
- snoble
- · Replies 11 ·
Undergrad Proving |X + Y|² + |X - Y|² = 2|X|² + 2|Y|²
- EvLer
- · Replies 2 ·
Graduate Operator change of basis (QM / QI)
- James Jackson
- · Replies 6 ·
Graduate Why does the recursive sequence R_n converge to k² for x = k² - k + 1?
- bomba923
- · Replies 11 ·
Graduate Intersection of cyclic subgroups
- Chen
- · Replies 2 ·
Graduate Find all the homomorphisms from Z12 to Z6?
- kara1424
- · Replies 2 ·
Graduate Prove/Disprove: F1 and F2 Isomorphic as Fields
- T-O7
- · Replies 5 ·
Graduate Proof: S_n is Not Abelian for n >= 3
- TsunamiJoe
- · Replies 6 ·
Graduate Can Polynomial Maps and Ideals Demonstrate a Ring Isomorphism in Finite Fields?
- grimster
- · Replies 2 ·
Undergrad System of three equations in row echelon form not consistent
- Exulus
- · Replies 4 ·
Graduate Writing Natural Numbers: A Unique Expression Using Powers of 2 and Odd Numbers
- gravenewworld
- · Replies 8 ·
Graduate Can Any Unitary Matrix Be Expressed as e^A?
- bor0000
- · Replies 11 ·
Graduate Finite groups and order of their elements
- Chen
- · Replies 8 ·
Graduate Can a natural isomorphism be viewed as a functor?
- Hurkyl
- · Replies 8 ·
Undergrad What are the properties and connections between bit strings and graph theory?
- miraclepie
- · Replies 2 ·
Graduate Origin of Numbers: Pythagorean Theory
- arivero
- · Replies 6 ·
Graduate Prove Endomorphism Ring of Simple Module is a Field
- Don Aman
- · Replies 13 ·
High School Is the number 2.3 even or odd?
- The Rev
- · Replies 22 ·
Graduate Generate All Permutations of Sn from An and 1 Odd Permutation
- gravenewworld
- · Replies 2 ·
Undergrad Are Skew-Symmetric Matrices a Subspace of Mat2x2(ℝ)?
- mang733
- · Replies 4 ·
Graduate Isomorphisms of Hom spaces for direct sums of modules
- JdotAckdot
- · Replies 2 ·
Undergrad Can Infinity Divided by Zero Yield One?
- B-Con
- · Replies 14 ·
Graduate Right ideals in M(n,n) and their relation to column spaces
- Gale
- · Replies 5 ·
Graduate Proving Equality of Fields with Distinct Primes in Z
- T-O7
- · Replies 2 ·
Graduate Is the Kernel of a Field Homomorphism Trivial or Isomorphic to the Field?
- ti89fr33k
- · Replies 2 ·
Undergrad Understanding Multiplicity and Dimension in Eigenvectors
- EvLer
- · Replies 5 ·
High School Is (A²)×B the same as A×A×B?
- C0nfused
- · Replies 5 ·
Graduate Finding irreducible representations for C2, C3 and C3v groups
- PhysKid24
- · Replies 4 ·
Undergrad Solutions to x^2==22(mod103) in Z103
- clueles
- · Replies 4 ·
Undergrad Solving f(x)=3x^2+7x=5 for m=23 and m=25 using Completing the Square
- clueles
- · Replies 2 ·
Graduate Prove that inv(G) is a group. G is a monoid
- grimster
- · Replies 6 ·
Graduate Proving K/F is Separable Extension
- Palindrom
- · Replies 3 ·
Graduate Is T(inv)(0) a Subspace of V and T(V) a Subspace of W?
- mang733
- · Replies 4 ·
Graduate How do you prove Aut_n(K) is isomorphic to S_q^n?
- grimster
- · Replies 12 ·
Undergrad Proving Congruence: (p-1, k) ≡ (-1)^k (mod p)
- katatonia
- · Replies 5 ·
Undergrad Solution Sets and Linear Equations
- e(ho0n3
- · Replies 3 ·
Graduate O(ab) when o(a) and o(b) are relatively prime
- Chen
- · Replies 11 ·