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 Why is b considered an element of R^m in the Ax=b theorem?
- bonfire09
- · Replies 3 ·
Graduate How do you take the logarithm of a 2x2 matrix with non-zero entries?
- jhendren
- · Replies 2 ·
High School How Do You Find the Inner Product of Vectors in Polar Coordinates?
- spaderdabomb
- · Replies 2 ·
Undergrad How Do You Find the Equation of a Plane Given a Point and a Perpendicular Line?
- salistoun
- · Replies 2 ·
Undergrad Matrix corresponding to linear transformation is invertible iff it is onto?
- Aziza
- · Replies 1 ·
Graduate Proving the Group Properties of M, the Set of Nth Roots of Unity
- ustus
- · Replies 2 ·
Finding the Inverse of Symmetric Matrices with Non-Real Coefficients
- OhMyMarkov
- · Replies 2 ·
Graduate Understanding Vector Spaces: Properties and Applications
- member 392791
- · Replies 6 ·
Graduate Is it possible to define a basis for the space of continuous functions?
- Boorglar
- · Replies 7 ·
Graduate Transforming a matrix to orthogonal one
- onako
- · Replies 4 ·
Graduate Identity in Subcategory C': Does it Coincide with Identity in Category C?
- SVD
- · Replies 1 ·
Undergrad Kernel and Range: Understanding Linear Transformation in Algebra
- matqkks
- · Replies 2 ·
Why study the kernel and range of linear transformations
- matqkks
- · Replies 1 ·
Undergrad Simple Proof for A-H Array Puzzle
- ramsey2879
- · Replies 3 ·
Undergrad Can you prove the formula for projection of a vector using dot products?
- Bipolarity
- · Replies 1 ·
Graduate Proving a relation between cross and dot products
- Bipolarity
- · Replies 1 ·
Graduate Consecutive integers divisible by a set of Primes
- axelmorack
- · Replies 4 ·
Undergrad Why do we use double pipes to represent the norm of a vector?
- Ashiataka
- · Replies 6 ·
Graduate Mapping Conditions in Transformational Space
- CluelessEngg
- · Replies 1 ·
Undergrad Proving that planes are parallel
- Bipolarity
- · Replies 7 ·
If G is the union of 3 of its subgroups, show that they each have index 2
- oblixps
- · Replies 4 ·
Is Goldbach's Conjecture Finally Solved?
- DeadOriginal
- · Replies 3 ·
Graduate Question on a proof by induction
- mnb96
- · Replies 2 ·
Graduate Can You Find the Unique Solution to These Simultaneous Equations?
- FeDeX_LaTeX
- · Replies 2 ·
Undergrad Vector cross product with coefficients
- Stickybees
- · Replies 2 ·
Graduate Matrices Formula for 10 by 10 Matrices
- BionicBiceps
- · Replies 10 ·
Graduate Where do the vector space axioms come from?
- JamesGold
- · Replies 5 ·
Undergrad What is the significance of the field Z₂ in mathematics?
- Max.Planck
- · Replies 2 ·
Undergrad Is there such a matrix operation
- Wolfgang2b
- · Replies 2 ·
Graduate Question on conjugate closure of subgroups
- mnb96
- · Replies 2 ·
High School Simple Proof That Division By Zero Is Impossible
- Poolala
- · Replies 6 ·
Undergrad Evaluate this algebraic expression f(a,b)
- epsi00
- · Replies 3 ·
Undergrad What Is the Solution Space for Ax=b in Linear Algebra?
- dumbQuestion
- · Replies 2 ·
Undergrad What is the importance of linear transformations in linear algebra?
- matqkks
- · Replies 4 ·
Graduate Is the sum of (m!/n!)^a countably or uncountably infinite?
- Eval
- · Replies 9 ·
Undergrad Understanding basis and dimension
- dumbQuestion
- · Replies 5 ·
Graduate Using Zelator's theorem to prove x³ + y³ = z³ has no integer solutions
- epsi00
- · Replies 1 ·
Undergrad Quick check of 4 term polynomial factorised
- Taylor_1989
- · Replies 3 ·
Undergrad Why is n² congruent to 0, 1, 2, or 4 mod 7 for any integer n?
- bonfire09
- · Replies 17 ·
Graduate Diagonolizing 5x5 Matrix by Hand
- xWaffle
- · Replies 12 ·
Undergrad Checking if scalar multiplication axioms hold for different scalars and vectors
- ryan8642
- · Replies 2 ·
Using linear systems to solve problems (1)
- bkan21
- · Replies 2 ·
Why introduce linear transformations before matrices
- matqkks
- · Replies 2 ·
Undergrad Does zero vector only exist in dim 0?
- pob1212
- · Replies 2 ·
Undergrad Finding if an integer is odd through Riemann or some function?
- caljuice
- · Replies 13 ·
Undergrad How Do You Solve This Linear System and Identify Free and Basic Variables?
- amcgl064
- · Replies 1 ·
Determining Basic and Free Variables in a Linear System
- amcgl064
- · Replies 1 ·
Undergrad Diagonalizing a Matrix: Implications of Double Eigenvalues
- icetea555
- · Replies 4 ·
Undergrad Unsure Which Method To Solve Linear System Was Used
- Illuminerdi
- · Replies 7 ·
Graduate Is it possible to linearize the non-linear equation in this linear programming?
- jack1234
- · Replies 1 ·
Undergrad Does a set need to be a subset to be a subspace?
- Max.Planck
- · Replies 3 ·
Graduate Solution of polynomial equations
- tom.stoer
- · Replies 5 ·
Graduate When Is L(S ∩ T) Not Equal to L(S) ∩ L(T)?
- TrapMuzik
- · Replies 1 ·
Undergrad Why do linear systems have zero, one, or infinite solutions?
- fisico30
- · Replies 7 ·
Undergrad What does badly scaled and nearly singular mean for a matrix?
- sunny110
- · Replies 14 ·
Graduate Find point coordinate on 3D circle knowing three points
- alaam2005
- · Replies 6 ·
Using linear systems to solve problems (4)
- bkan21
- · Replies 1 ·
Graduate Homogeneous Eqn of Line given 2 homogeneous pointspoints
- LouArnold
- · Replies 5 ·
Using linear systems to solve problems (3)
- bkan21
- · Replies 1 ·
Using linear systems to solve problems (5)
- bkan21
- · Replies 1 ·
Graduate Proving that the product of two full-rank matrices is full-rank
- leden
- · Replies 6 ·
High School Is there a largest prime number and does it disprove Goldbach's conjecture?
- Ferraridude
- · Replies 6 ·
High School Why does (Earth's speed + orbital seconds) / speed of light equal Earth's speed?
- JackWilkinson
- · Replies 5 ·
Undergrad Proof- Vector fields form vector space
- deanachuz
- · Replies 2 ·
Graduate Are There Only 3 Nontrivial Subgroups of Zp x Zp?
- carrie.lugo
- · Replies 2 ·
Graduate How Do the Riemann Zeta and Dirichlet Eta Functions Interact?
- arivero
- · Replies 3 ·
Graduate Does v = u + w hold for all u in U when V = U ⊕ W?
- omoplata
- · Replies 2 ·
Graduate Rotation from axis to axis in 4 dimensions
- Matt Benesi
- · Replies 2 ·
Undergrad Error in Leon's database search example dimensions
- schaefera
- · Replies 4 ·
Undergrad Why is QR factorization useful and important?
- matqkks
- · Replies 1 ·
Graduate What is the Mathematical Definition of the Pauli Vector?
- Grufey
- · Replies 4 ·
Why is QR factorization useful and important?
- matqkks
- · Replies 1 ·
Maximal Ideal of Z[sqrt(-19)]: Showing Why (2, 1+sqrt(-19)) Works
- Jooolz
- · Replies 4 ·
Graduate Decompose matrix into outer product of vectors
- Pacopag
- · Replies 6 ·
Graduate Is 11 a Prime in the Non-UFD Ring Z[sqrt{-5}]?
- bessletama
- · Replies 2 ·
Undergrad Is it worse an over or an under determined system of linear equations?
- fisico30
- · Replies 15 ·
Undergrad Need help understanding Linear algebra proofs (and linear algebra in general)
- Sysman
- · Replies 10 ·
Graduate Showing that the normalized eigenvector for a distinct eigenvalue is unique
- randomafk
- · Replies 4 ·
Undergrad Why is the dot product of two vectors A·B = ABcosθ?
- cytochrome
- · Replies 12 ·
Undergrad Why Does Solving Matrices Lead to Incorrect Variable Identification?
- Taylor_1989
- · Replies 2 ·
How Do You Calculate the Determinant of a Matrix in Linear Algebra?
- Chipset3600
- · Replies 3 ·
Graduate Is the ABC Conjecture Solved? New Proof Claims Deep Connection to Prime Numbers
- Dragonfall
- · Replies 2 ·
Undergrad Question regarding cross products and determinants
- Salamon
- · Replies 2 ·
Graduate Why does A*I*inverse(A) create a projection matrix?
- pamparana
- · Replies 1 ·
Graduate Transforming between square matrices of different order
- Mårten
- · Replies 4 ·
Graduate What is the mysterious identity that holds for primes and certain composites?
- ramsey2879
- · Replies 11 ·
Graduate Is h(n) - f(n) in o(g(n)) Given f(n) in o(g(n)) and g(n) in O(H(n))?
- ammoun
- · Replies 3 ·
Undergrad Which Mathematicians Pioneered Prime Numbers for Cryptography?
- phospho
- · Replies 2 ·
Graduate Determinant of Transpose Operator
- sponsoredwalk
- · Replies 9 ·
Why find angles and distances between polynomials in inner product spaces
- matqkks
- · Replies 1 ·
Graduate Is Pi divided by E rational, and what other irrational numbers exist?
- Jedi_Sawyer
- · Replies 15 ·
Graduate Inner product of polynomials
- matqkks
- · Replies 1 ·
Can You Solve These Advanced Determinant Problems Involving Matrices?
- Yankel
- · Replies 5 ·
Undergrad Why must graphs in sums have only loops and no knots?
- LagrangeEuler
- · Replies 1 ·
Undergrad What model best fits this data and why?
- spacecadeta
- · Replies 4 ·
Does a'a = 1 if aa' = 1 and a' is unique?
- Fantini
- · Replies 4 ·
Undergrad Proving Linear Manipulation to Reduce to GCD of Two Numbers
- Avichal
- · Replies 6 ·
Undergrad Formula for sequence 1,2,1,2,3,4,1,2,3,4,5,6,
- spiritzavior
- · Replies 10 ·
Undergrad Infinite solutions to homogeneous system?
- hivesaeed4
- · Replies 2 ·
Graduate Basis of a subspace and dimension question
- clurt
- · Replies 1 ·