Linear and Abstract Algebra Forum

Post thread
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.
Equivalence of Subspace Statements
  • mathmari
  • · Replies 9 ·
Replies
9
Row echelon form : Can the first column contain only zeros?
  • mathmari
  • · Replies 14 ·
Replies
14
Graduate What is the Corollary of the Nucleus and Image Theorem?
  • Portuga
  • · Replies 2 ·
Replies
2
M has the unit matrix at the upper left side and zero everywhere else
  • mathmari
  • · Replies 8 ·
Replies
8
Rank of composition of linear maps
  • mathmari
  • · Replies 7 ·
Replies
7
Graduate Eigenvalues of block matrix/Related non-linear eigenvalue problem
  • pasmith
  • · Replies 1 ·
Replies
1
How Are the Vectors $z_1$, $z_2$, and $z_3$ Created in the Span?
  • karush
  • · Replies 1 ·
Replies
1
Undergrad What is the logarithm of the derivative operator?
  • Anixx
  • · Replies 10 ·
Replies
10
T31 vector subtraction is not commutative and not associative.
  • karush
  • · Replies 5 ·
Replies
5
Undergrad Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix
  • The Head
  • · Replies 3 ·
Replies
3
Does Linear Independence in V Imply the Same in W?
  • mathmari
  • · Replies 24 ·
Replies
24
Undergrad How to Prove a Congruence Relation for Prime Numbers?
  • DaTario
  • · Replies 17 ·
Replies
17
Graduate Topology on a space of Lie algebras
  • fresh_42
  • · Replies 2 ·
Replies
2
Undergrad Taylor expansion of an unknown function
  • Alex_F
  • · Replies 5 ·
Replies
5
High School What is the cross product of two vectors?
  • erocored
  • · Replies 32 ·
2
Replies
32
Undergrad Do These Vectors Span V?
  • Mayhem
  • · Replies 13 ·
Replies
13
If 2 columns are identical is there infinite solutions
  • karush
  • · Replies 4 ·
Replies
4
Solving Systems of Six Equations with Nine Variables
  • karush
  • · Replies 1 ·
Replies
1
307w.WLCA.C10 computations are linear?
  • karush
  • · Replies 3 ·
Replies
3
Undergrad ##(p^k -1) \equiv X \mbox{(mod p)}## via Wilson's theorem
  • DaTario
  • · Replies 2 ·
Replies
2
Construct 3 Augmented Matrices for Linear Systems
  • karush
  • · Replies 2 ·
Replies
2
307w.43.M40 find corresponding 3 scalars
  • karush
  • · Replies 1 ·
Replies
1
Undergrad Why doesn't sinc(x) converge to Gaussian upon repeated convolution?
  • skynelson
  • · Replies 1 ·
Replies
1
Graduate What is the difference between groups SU(n) and SO(n,C)?
  • LagrangeEuler
  • · Replies 12 ·
Replies
12
Undergrad Rodrigues' rotation formula from SO(3) comutator properties
  • sergiokapone
  • · Replies 3 ·
Replies
3
High School Orthogonal Projections: Same Thing or Not?
  • Isaac0427
  • · Replies 4 ·
Replies
4
Undergrad Solving a complex linear system with parameters
  • iopz
  • · Replies 11 ·
Replies
11
Undergrad Domain of convolution vs. domain of Fourier transforms
  • skynelson
  • · Replies 3 ·
Replies
3
311.1.5.19 parametric equation of the line through a parallel to b.
  • karush
  • · Replies 1 ·
Replies
1
Graduate Understanding the Relationship between Orthogonal and Unitary Groups
  • LagrangeEuler
  • · Replies 13 ·
Replies
13
Linearly Dependent Vectors: Find h Value and Justify
  • karush
  • · Replies 4 ·
Replies
4
Graduate Matrix multiplication, Orthogonal matrix, Independent parameters
  • LagrangeEuler
  • · Replies 3 ·
Replies
3
High School Graph of ax+by=c: How a,b,c Affects Graph
  • sahilmm15
  • · Replies 3 ·
Replies
3
Graduate Is the notion of elementary function a fluid concept among algebras?
  • Anixx
  • · Replies 2 ·
Replies
2
Graduate Mathematical term for physicist's "Lattice Theory"?
  • Stephen Tashi
  • · Replies 10 ·
Replies
10
311.1.7.9 For what values of h is v_3 in Span {v_1,v_2,v_3}
  • karush
  • · Replies 3 ·
Replies
3
Undergrad Proof concerning the Four Fundamental Spaces
  • Peter_Newman
  • · Replies 14 ·
Replies
14
311.1.5.14 Use vectors to describe this set as a line in R^4
  • karush
  • · Replies 4 ·
Replies
4
Undergrad If L is diagonalizable, algebraic & geometric multiplicities are equal
  • JD_PM
  • · Replies 4 ·
Replies
4
Undergrad Understanding Unfaithful Representations of Z_2 in the Caley Table
  • LagrangeEuler
  • · Replies 16 ·
Replies
16
311.1.5.17 geometric description
  • karush
  • · Replies 2 ·
Replies
2
Is b a linear combination of a1, a2, and a3?
  • karush
  • · Replies 7 ·
Replies
7
Undergrad Decomposing arbitrary representations
  • StaticZero
  • · Replies 2 ·
Replies
2
LU decomposition: With or without pivoting?
  • mathmari
  • · Replies 2 ·
Replies
2
Graduate Error in Sadri Hassani's Mathematical Physics
  • cleaf
  • · Replies 29 ·
Replies
29
High School A problem involving direction cosines (Vector Algebra)
  • sahilmm15
  • · Replies 3 ·
Replies
3
311.1.3.19 find h and k in the system
  • karush
  • · Replies 1 ·
Replies
1
311.3.2.16 Find the determinant with variables a b c d e f g h i
  • karush
  • · Replies 4 ·
Replies
4
Undergrad What is the Dimension of SO(3) with Constraint det(O) = 1?
  • shinobi20
  • · Replies 6 ·
Replies
6
High School What is the identity element in the group {2,4,6,8} under multiplication mod 10?
  • LCSphysicist
  • · Replies 9 ·
Replies
9
Undergrad Poincaré algebra and quotient group
  • LCSphysicist
  • · Replies 1 ·
Replies
1
307.1.1 Use row reduction on the appropriate augmented
  • karush
  • · Replies 5 ·
Replies
5
Undergrad Group and Identity: Proving (12)(34)² = (12)(34)
  • LCSphysicist
  • · Replies 2 ·
Replies
2
311.1.3.2 u+v and u-2v and tikx?
  • karush
  • · Replies 9 ·
Replies
9
Proving $x-1$ is a Factor of $P(x)$ with Polynomials
  • anemone
  • · Replies 1 ·
Replies
1
Undergrad Invertible Polynomials: P2 (R) → P2 (R)
  • username123456789
  • · Replies 1 ·
Replies
1
Graduate How Do You Apply Noether Normalization to a Polynomial Ring Ideal?
  • gurilupi
  • · Replies 14 ·
Replies
14
Undergrad Determine the limit in a Markov process over time
  • Karl Karlsson
  • · Replies 17 ·
Replies
17
Proving Orthogonal Projection of Triangle V, v'_{1}
  • rannasquaer
  • · Replies 1 ·
Replies
1
Symmetry Operations of a Cube: Geometric Descriptions and Matrix Representations
  • mathmari
  • · Replies 31 ·
2
Replies
31
Subsets of $\mathbb{R}^2$ Satisfying S2 and S3 but Not S1: Empty Set
  • mathmari
  • · Replies 6 ·
Replies
6
Solve Sets of Form $v+X$ in $\mathbb{R}^2$
  • mathmari
  • · Replies 5 ·
Replies
5
311.2.2.6 use inverse matrix to solve system of equations
  • karush
  • · Replies 2 ·
Replies
2
Undergrad Base Pi Integers: Isomorphism with Rationals?
  • Atran
  • · Replies 33 ·
2
Replies
33
Does the Cosine Rule Apply to Vector Addition in 3-D?
  • WMDhamnekar
  • · Replies 2 ·
Replies
2
Set is closed as for multiplication of matrices
  • mathmari
  • · Replies 16 ·
Replies
16
B=Q^TAQ has a LU decomposition
  • mathmari
  • · Replies 12 ·
Replies
12
Undergrad Showing that a set of differentiable functions is a subspace of R
  • Mayhem
  • · Replies 19 ·
Replies
19
How to Choose the Right Running Shoes for You
  • Joelly
  • · Replies 1 ·
Replies
1
Tips for Eating Healthy on a Budget
  • Joelly
  • · Replies 2 ·
Replies
2
What is the form of that matrix?
  • mathmari
  • · Replies 8 ·
Replies
8
Undergrad P-adic valuation expression for a given natural number
  • DaTario
  • · Replies 9 ·
Replies
9
High School In algebra what does x represent?
  • laymanhobbist
  • · Replies 26 ·
Replies
26
Graduate Algebra of divergent integrals
  • Anixx
  • · Replies 28 ·
Replies
28
Undergrad Definiteness of a nonsymmetric matrix
  • Mathsadness
  • · Replies 4 ·
Replies
4
Proving Zp is a Vector Space for Prime p
  • THEcj39
  • · Replies 4 ·
Replies
4
Undergrad Proving linear independence of two functions in a vector space
  • fatpotato
  • · Replies 5 ·
Replies
5
Graduate Order of group, Order of element
  • LagrangeEuler
  • · Replies 13 ·
Replies
13
For which c is there 1/0 solution?
  • mathmari
  • · Replies 2 ·
Replies
2
Undergrad How Are Dual Vectors and Covectors Related in Vector Spaces?
  • Kaguro
  • · Replies 15 ·
Replies
15
Linear system of equations: Echelon form/Solutions
  • mathmari
  • · Replies 3 ·
Replies
3
Undergrad The Value and Applications of Group Theory in Mathematics
  • trees and plants
  • · Replies 42 ·
2
Replies
42
Undergrad Is there a theorem that a set of binary swaps can affect any permutation?
  • swampwiz
  • · Replies 8 ·
Replies
8
Calculating the Inverse Matrix for a 3x3 Matrix
  • karush
  • · Replies 5 ·
Replies
5
Undergrad Is Complex Differentiation Defined for Linear Transformations?
  • r731
  • · Replies 4 ·
Replies
4
Solving System of Equations: xy, yz, zx
  • solakis1
  • · Replies 3 ·
Replies
3
Graduate How to investigate a transformation that might form a Lie group?
  • LieToMe
  • · Replies 27 ·
Replies
27
311.1.5.12 Ax=0 in parametric vector form
  • karush
  • · Replies 7 ·
Replies
7
Is G/G isomorphic to the trivial group? A proof for G/G\cong \{e\}
  • lemonthree
  • · Replies 1 ·
Replies
1
Undergrad Decomposition per the Fundamental Theorem of Finite Abelian Groups
  • jstrunk
  • · Replies 13 ·
Replies
13
Graduate Finite non-abelian group of the order pq, pq primes
  • Sportin' Life
  • · Replies 2 ·
Replies
2
-311.1.5.8 Ax=b in parametric vector form,
  • karush
  • · Replies 7 ·
Replies
7
311.1.5.5 homogeneous systems in parametric vector form.
  • karush
  • · Replies 2 ·
Replies
2
Undergrad Prove that dim(V⊗W)=(dim V)(dim W)
  • Karl Karlsson
  • · Replies 2 ·
Replies
2
Undergrad Hermitian Operators and Non-Orthogonal Bases: Exploring Infinite Spaces
  • LCSphysicist
  • · Replies 2 ·
Replies
2
Undergrad Does anyone really understand what's really going on with this video?
  • swampwiz
  • · Replies 7 ·
Replies
7
Undergrad What is the definition of trace for n-indexed tensor in group theory?
  • dontknow
  • · Replies 1 ·
Replies
1
Undergrad Rotational invariance of cross product matrix operator
  • Filip Larsen
  • · Replies 7 ·
Replies
7
Undergrad Trying to get a better understanding of the quotient V/U in linear algebra
  • Karl Karlsson
  • · Replies 10 ·
Replies
10
Undergrad Understanding Algebraic Numbers & Proving Them
  • swampwiz
  • · Replies 1 ·
Replies
1