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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Graduate Rank(AB) = Rank(A)Rank(B)?The Rank Product Theorem for Matrices
- itpro
- · Replies 1 ·
Undergrad Why Must Free Variables Be Non-Leading in Linear Systems?
- skwey
- · Replies 2 ·
Graduate Why is a Linear Transformation a Type-(1,1) Tensor?
- marschmellow
- · Replies 6 ·
Graduate Proving the Simplicity of a Group of Order 36 Using Sylow Subgroups
- Bachelier
- · Replies 9 ·
Graduate Let G = D12, given by generators a,b with |a|=6, |b|=2, and ba=a-1b.
- Bachelier
- · Replies 2 ·
Undergrad General function that represents a series of 1 and 0
- Emilijo
- · Replies 28 ·
Graduate A Unitary Matrix and Hermitian Matrix
- Demon117
- · Replies 2 ·
Undergrad What is the difference between these two operations?
- zheng89120
- · Replies 1 ·
Graduate Multiplicative closure for subring test?
- phasic
- · Replies 6 ·
Graduate Quaternion Polynomial Equation
- alexfloo
- · Replies 3 ·
Graduate Are Intersections of Sylow p-Groups Always Trivial?
- Bachelier
- · Replies 4 ·
Graduate How to Find and Prove All Distinct Ideals of a Ring?
- me@math
- · Replies 1 ·
Undergrad Difference among types of bases.
- smithnya
- · Replies 3 ·
Graduate Why is G abelian if |G/Z(G)|=p with p prime?
- Menelaus
- · Replies 11 ·
Undergrad Is diagonalizability necessary for computing the matrix exponential?
- AirForceOne
- · Replies 2 ·
Graduate What are Quotient Spaces and How Are They Used in Algebra and Topology?
- flyerpower
- · Replies 3 ·
Graduate Why must inner product spaces be over the field of real or complex numbers?
- cavalier
- · Replies 4 ·
Graduate What are the eigenfunctions of the spherical Fourier transform?
- christianjb
- · Replies 8 ·
Undergrad Polytopes: Understanding Linear vs Affine Spans
- arthurhenry
- · Replies 2 ·
Graduate Unique Factorisation Domains/Fields
- Zoe-b
- · Replies 6 ·
Undergrad Matrix Invertibility and the Minimal Polynomial
- jonnyc1003
- · Replies 10 ·
Graduate Is {u+v+w, v+w, w} Also a Basis for V?
- aortizmena
- · Replies 8 ·
Graduate Why are ideals generated by 2, 4 and 8 the same in ring theory?
- General_Sax
- · Replies 2 ·
Graduate Cross product for complex vectors
- dimension10
- · Replies 4 ·
Graduate Diophantine equations of the form x^3-dy^3=1
- Mathguy15
- · Replies 3 ·
Undergrad Number of solutions for a homogeneous system Ax = 0
- anu914
- · Replies 2 ·
Graduate Prove that (a1*a2*...*an)^2 = e in a finite abelian group
- Ledger
- · Replies 6 ·
Undergrad What exactly does it mean for two points to be barycentrically independent?
- Mathguy15
- · Replies 4 ·
Graduate Certain and Curious Number Sequence
- Feryll
- · Replies 4 ·
Undergrad How can the period of a matrix be determined?
- helen01
- · Replies 12 ·
Graduate Do Diagonal Elements in Congruence Transformations Represent Eigenvalues?
- thoughtgaze
- · Replies 1 ·
Graduate Approximating the reals by rationals (Littlewood's Conjecture)
- funkstar
- · Replies 2 ·
Graduate How Do You Solve w=0.5(z+1/z) for Complex w?
- Macarenses
- · Replies 5 ·
Graduate Finding matrix A such that A*B=A where B is non-identity
- thinktank2
- · Replies 5 ·
Undergrad How can the square root of a large number be found without a calculator?
- Quark Itself
- · Replies 6 ·
High School Are these two matrices the same?
- Fry
- · Replies 1 ·
Graduate How to find the magnitude of this bivector?
- dimension10
- · Replies 12 ·
Graduate Understanding Group Orbits: A Wolfram Mathworld Example
- Ryker
- · Replies 5 ·
Graduate How to prove the linear indenpendency of an infinite set
- julypraise
- · Replies 3 ·
Graduate Would someone explain the class equation and its corrolaries for me?
- AdrianZ
- · Replies 4 ·
Graduate SUBSET K of elements in a group with finite distinct distinct conjugates
- Bachelier
- · Replies 1 ·
Graduate Some kind of mathematical formula that I obviously dont know about?
- M. next
- · Replies 8 ·
Undergrad Is an Orthonormal Set Necessarily Orthogonal?
- SeannyBoi71
- · Replies 1 ·
Graduate Relations between k and n for Proth primes
- pedja
- · Replies 2 ·
Graduate What Does Up to Isomorphism Really Mean?
- Bachelier
- · Replies 8 ·
Graduate Dimension of space composed of powers of a matrix
- Grothard
- · Replies 1 ·
Graduate (Linear Algebra) Distinct Eigenvalues of a Matrix
- Gg199
- · Replies 2 ·
Graduate Counter Example: Abelian Subgroup Not Normal
- Bachelier
- · Replies 1 ·
Graduate Using isomorphisms to transform polynomials to vectors.
- -Dragoon-
- · Replies 1 ·
Undergrad What is the Basis for a Row Reduced 3x3 Matrix in Linear Algebra?
- fellupahill
- · Replies 1 ·
Undergrad Easy method to show orthogonality of a matrix
- dapias09
- · Replies 2 ·
Graduate Why can't Sn be embedded into An+1?
- Coca_Cola
- · Replies 3 ·
Graduate Transforming Positive Definite Quadratic Forms: A Simplification Approach
- Office_Shredder
- · Replies 2 ·
Graduate Proving L is a normal extension of F
- ae1709
- · Replies 1 ·
Graduate Examples of normal and non-normal extensions of Q?
- ae1709
- · Replies 4 ·
Undergrad What do they mean by classify all groups of a certain order
- Bachelier
- · Replies 1 ·
Graduate Can K⊕K ≅ N⊕N Imply K ≅ N in Finite Abelian Groups?
- Bachelier
- · Replies 2 ·
Undergrad Invertibility and Diagonalizability
- 0pt618
- · Replies 9 ·
Graduate Subset of the indempotents of a ring
- pol92
- · Replies 3 ·
Graduate Simple definition of a Lie algebra?
- pellman
- · Replies 8 ·
Graduate Relationship of Basis to Dual Basis
- marschmellow
- · Replies 1 ·
Graduate Are There Unnormed Vector Spaces?
- zooxanthellae
- · Replies 11 ·
Undergrad Find Basis for Span: \vec{a_{1}} to \vec{a_{4}}
- ferry2
- · Replies 6 ·
Graduate If p is prime, prove the group (Zp*,x) has exactly one element of order 2.
- ae1709
- · Replies 3 ·
Graduate Wedge product coefficient convention in Bishop & Goldberg
- Rasalhague
- · Replies 1 ·
Graduate Irreducible polynomials over ring of integers
- pedja
- · Replies 5 ·
Undergrad Dijkstra's or A* for this situation
- eboyle12
- · Replies 1 ·
Graduate Evaluating a term in bra-ket notation
- cybla
- · Replies 2 ·
Graduate Q (the rationals) not free abelian yet iso to Z^2?
- TopCat
- · Replies 2 ·
Graduate Looking for Explanation of a Quotient Group
- "pi"mp
- · Replies 6 ·
Undergrad Solving Combinatorics: Finding the Number of Sets with Elements from A, B, and C
- Neitrino
- · Replies 1 ·
Graduate Do Functions of Commuting Operators Always Commute?
- McLaren Rulez
- · Replies 6 ·
High School Relationships of the number kind
- Cladinator
- · Replies 2 ·
Undergrad 2D Perspective xform using CSS 3D matrix?
- SporkInTucson
- · Replies 4 ·
Graduate Order of Automorphism and Abelian Groups
- RVP91
- · Replies 3 ·
Graduate How to find all elements of S4 that satisfy the equation x^4=e?
- AdrianZ
- · Replies 36 ·
Graduate A problem on finding orthogonal basis and projection
- visharad
- · Replies 5 ·
Graduate Determinant as a function of trace
- lukluk
- · Replies 3 ·
Graduate Proving Surjectivity of Mapping A_g:G ---> G for Automorphism
- RVP91
- · Replies 2 ·
Undergrad What Is the Kernel of a Subgroup?
- Ledger
- · Replies 8 ·
Graduate Proving Distance Between Plane and Point P
- batballbat
- · Replies 1 ·
Undergrad Why Ax=0 only has trivial solution
- georg gill
- · Replies 5 ·
Graduate Prove that a product of disjoint m-cycles is a power of a cycle
- Bachelier
- · Replies 4 ·
Undergrad Are All Groups Nonempty and How Does the Group Identity Factor In?
- blueberryfive
- · Replies 1 ·
High School Necessary But Not Sufficient Check For Addition
- LawrenceC
- · Replies 4 ·
Undergrad What is the relationship between determinant and inverse of a matrix?
- vilhelm
- · Replies 6 ·
Graduate Proving W^a=0 in Tensor Multiplication: A critical analysis
- PhyPsy
- · Replies 2 ·
Graduate Solving Flip It: How Can I Solve the Game Using Mathematical Equations?
- TylerH
- · Replies 1 ·
Graduate How to multiply these summations ?
- praecox
- · Replies 1 ·
Undergrad Scaling Augmented Matrices: Is My Thinking Correct?
- jeremy222
- · Replies 2 ·
Graduate Do subgrps inherent their group properties
- Bachelier
- · Replies 4 ·
Undergrad Finding Subgroups of certain orders
- RVP91
- · Replies 3 ·
Graduate Can the Cross Product be Generalized Using the Dot Product?
- Damidami
- · Replies 4 ·
Graduate Why Aren't Non-Continuous Functions in an Interval Considered a Linear Space?
- batballbat
- · Replies 9 ·
Undergrad Solving tan(x)=kx/z² for constant k given x and z
- surajt88
- · Replies 3 ·
Graduate When does x^2 ≡ a (mod p) have solutions?
- demonelite123
- · Replies 5 ·
Undergrad Is Zero Division a Matter of Convention or Something Else?
- narrator
- · Replies 6 ·
Undergrad Can Vectors Project Onto an Arbitrary Line?
- batballbat
- · Replies 1 ·
Undergrad Proving linear dependence when adding a vector to a basis
- autre
- · Replies 2 ·
Undergrad Arbitrary digit of an exponential number
- cap.r
- · Replies 2 ·