Linear and Abstract Algebra Forum

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.

Threads

Graduate What physical meaning can the “determinant” of a divergency have?

  • Anixx
  • · Replies 3 ·
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3

Give a basis to get the specific matrix M

  • mathmari
  • · Replies 34 ·
2
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34

Equivalence of Subspace Statements

  • mathmari
  • · Replies 9 ·
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9

Can the first column of a row echelon form contain only zeros?

  • mathmari
  • · Replies 14 ·
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14

Graduate What is the Corollary of the Nucleus and Image Theorem?

  • Portuga
  • · Replies 2 ·
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2

M has the unit matrix at the upper left side and zero everywhere else

  • mathmari
  • · Replies 8 ·
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8

Rank of composition of linear maps

  • mathmari
  • · Replies 7 ·
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7

Graduate Eigenvalues of block matrix/Related non-linear eigenvalue problem

  • pasmith
  • · Replies 1 ·
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1

How Are the Vectors $z_1$, $z_2$, and $z_3$ Created in the Span?

  • karush
  • · Replies 1 ·
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1

Undergrad What is the logarithm of the derivative operator?

  • Anixx
  • · Replies 10 ·
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10

T31 vector subtraction is not commutative and not associative.

  • karush
  • · Replies 5 ·
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5

Undergrad Meaning of Third Eigenvalue in a Tilted Ellipse in a 3x3 Matrix

  • The Head
  • · Replies 3 ·
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3

Does Linear Independence in V Imply the Same in W?

  • mathmari
  • · Replies 24 ·
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24

Undergrad How to Prove a Congruence Relation for Prime Numbers?

  • DaTario
  • · Replies 17 ·
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17

Graduate Topology on a space of Lie algebras

  • fresh_42
  • · Replies 2 ·
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2

Undergrad Taylor expansion of an unknown function

  • Alex_F
  • · Replies 5 ·
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5

High School What is the cross product of two vectors?

  • erocored
  • · Replies 32 ·
2
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32

Undergrad Do These Vectors Span V?

  • Mayhem
  • · Replies 13 ·
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13

If 2 columns are identical is there infinite solutions

  • karush
  • · Replies 4 ·
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4

Solving Systems of Six Equations with Nine Variables

  • karush
  • · Replies 1 ·
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1

307w.WLCA.C10 computations are linear?

  • karush
  • · Replies 3 ·
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3

Undergrad ##(p^k -1) \equiv X \mbox{(mod p)}## via Wilson's theorem

  • DaTario
  • · Replies 2 ·
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2

Construct 3 Augmented Matrices for Linear Systems

  • karush
  • · Replies 2 ·
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2

307w.43.M40 find corresponding 3 scalars

  • karush
  • · Replies 1 ·
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1

Undergrad Why doesn't sinc(x) converge to Gaussian upon repeated convolution?

  • skynelson
  • · Replies 1 ·
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1

Graduate What is the difference between groups SU(n) and SO(n,C)?

  • LagrangeEuler
  • · Replies 12 ·
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12

Undergrad Rodrigues' rotation formula from SO(3) comutator properties

  • sergiokapone
  • · Replies 3 ·
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3

High School Orthogonal Projections: Same Thing or Not?

  • Isaac0427
  • · Replies 4 ·
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4

Undergrad Solving a complex linear system with parameters

  • iopz
  • · Replies 11 ·
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11

Undergrad Domain of convolution vs. domain of Fourier transforms

  • skynelson
  • · Replies 3 ·
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3

311.1.5.19 parametric equation of the line through a parallel to b.

  • karush
  • · Replies 1 ·
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1

Graduate Why does diagonalizing SO(2) matrices give U(1) elements?

  • LagrangeEuler
  • · Replies 13 ·
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13

Linearly Dependent Vectors: Find h Value and Justify

  • karush
  • · Replies 4 ·
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4

Graduate Matrix multiplication, Orthogonal matrix, Independent parameters

  • LagrangeEuler
  • · Replies 3 ·
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3

High School Graph of ax+by=c: How a,b,c Affects Graph

  • sahilmm15
  • · Replies 3 ·
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3

Graduate Is the notion of elementary function a fluid concept among algebras?

  • Anixx
  • · Replies 2 ·
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2

Graduate Mathematical term for physicist's "Lattice Theory"?

  • Stephen Tashi
  • · Replies 10 ·
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10

311.1.7.9 For what values of h is v_3 in Span {v_1,v_2,v_3}

  • karush
  • · Replies 3 ·
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3

Undergrad Proof concerning the Four Fundamental Spaces

  • Peter_Newman
  • · Replies 14 ·
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14

311.1.5.14 Use vectors to describe this set as a line in R^4

  • karush
  • · Replies 4 ·
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4

Undergrad Proving algebraic equals geometric multiplicity for diagonalizable operators

  • JD_PM
  • · Replies 4 ·
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4

Undergrad Understanding Unfaithful Representations of Z_2 in the Caley Table

  • LagrangeEuler
  • · Replies 16 ·
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16

311.1.5.17 geometric description

  • karush
  • · Replies 2 ·
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2

Is b a linear combination of a1, a2, and a3?

  • karush
  • · Replies 7 ·
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7

Undergrad Decomposing arbitrary representations

  • StaticZero
  • · Replies 2 ·
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2

LU decomposition: With or without pivoting?

  • mathmari
  • · Replies 2 ·
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2

Graduate Error in Sadri Hassani's Mathematical Physics

  • cleaf
  • · Replies 29 ·
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29

High School A problem involving direction cosines (Vector Algebra)

  • sahilmm15
  • · Replies 3 ·
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3

311.1.3.19 find h and k in the system

  • karush
  • · Replies 1 ·
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1

311.3.2.16 Find the determinant with variables a b c d e f g h i

  • karush
  • · Replies 4 ·
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4

Undergrad What is the Dimension of SO(3) with Constraint det(O) = 1?

  • shinobi20
  • · Replies 6 ·
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6

High School What is the identity element in the group {2,4,6,8} under multiplication mod 10?

  • LCSphysicist
  • · Replies 9 ·
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9

Undergrad Poincaré algebra and quotient group

  • LCSphysicist
  • · Replies 1 ·
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1

307.1.1 Use row reduction on the appropriate augmented

  • karush
  • · Replies 5 ·
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5

Undergrad Group and Identity: Proving (12)(34)² = (12)(34)

  • LCSphysicist
  • · Replies 2 ·
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2

311.1.3.2 u+v and u-2v and tikx?

  • karush
  • · Replies 9 ·
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9

Proving $x-1$ is a Factor of $P(x)$ with Polynomials

  • anemone
  • · Replies 1 ·
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1

Undergrad Invertible Polynomials: P2 (R) → P2 (R)

  • username123456789
  • · Replies 1 ·
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1

Graduate How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

  • gurilupi
  • · Replies 14 ·
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14

Undergrad Determine the limit in a Markov process over time

  • Karl Karlsson
  • · Replies 17 ·
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17

Proving Orthogonal Projection of Triangle V, v'_{1}

  • rannasquaer
  • · Replies 1 ·
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1

Finding matrix representations for cube symmetries

  • mathmari
  • · Replies 31 ·
2
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31

Subsets of $\mathbb{R}^2$ Satisfying S2 and S3 but Not S1: Empty Set

  • mathmari
  • · Replies 6 ·
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6

Solve Sets of Form $v+X$ in $\mathbb{R}^2$

  • mathmari
  • · Replies 5 ·
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5

311.2.2.6 use inverse matrix to solve system of equations

  • karush
  • · Replies 2 ·
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2

Undergrad Is the group of base π integers isomorphic to the rationals?

  • Atran
  • · Replies 33 ·
2
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33

Does the Cosine Rule Apply to Vector Addition in 3-D?

  • WMDhamnekar
  • · Replies 2 ·
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2

Set is closed as for multiplication of matrices

  • mathmari
  • · Replies 16 ·
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16

B=Q^TAQ has a LU decomposition

  • mathmari
  • · Replies 12 ·
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12

Undergrad Showing that a set of differentiable functions is a subspace of R

  • Mayhem
  • · Replies 19 ·
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19

How to Choose the Right Running Shoes for You

  • Joelly
  • · Replies 1 ·
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1

Eating healthy on a budget

  • Joelly
  • · Replies 2 ·
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2

What is the form of that matrix?

  • mathmari
  • · Replies 8 ·
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8

Undergrad P-adic valuation expression for a given natural number

  • DaTario
  • · Replies 9 ·
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9

High School In algebra what does x represent?

  • laymanhobbist
  • · Replies 26 ·
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26

Graduate Algebra of divergent integrals

  • Anixx
  • · Replies 28 ·
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28

Undergrad Definiteness of a nonsymmetric matrix

  • Mathsadness
  • · Replies 4 ·
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4

Proving Zp is a Vector Space for Prime p

  • THEcj39
  • · Replies 4 ·
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4

Undergrad Proving linear independence of two functions in a vector space

  • fatpotato
  • · Replies 5 ·
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5

Graduate Order of group, Order of element

  • LagrangeEuler
  • · Replies 13 ·
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13

For which c is there 1/0 solution?

  • mathmari
  • · Replies 2 ·
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2

Undergrad How Are Dual Vectors and Covectors Related in Vector Spaces?

  • Kaguro
  • · Replies 15 ·
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15

Linear system of equations: Echelon form/Solutions

  • mathmari
  • · Replies 3 ·
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3

Undergrad The Value and Applications of Group Theory in Mathematics

  • trees and plants
  • · Replies 42 ·
2
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42

Undergrad Is there a theorem that a set of binary swaps can affect any permutation?

  • swampwiz
  • · Replies 8 ·
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8

Calculating the Inverse Matrix for a 3x3 Matrix

  • karush
  • · Replies 5 ·
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5

Undergrad Is Complex Differentiation Defined for Linear Transformations?

  • r731
  • · Replies 4 ·
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4

Solving System of Equations: xy, yz, zx

  • solakis1
  • · Replies 3 ·
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3

Graduate How to investigate a transformation that might form a Lie group?

  • LieToMe
  • · Replies 27 ·
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27

311.1.5.12 Ax=0 in parametric vector form

  • karush
  • · Replies 7 ·
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7

Is G/G isomorphic to the trivial group? A proof for G/G\cong \{e\}

  • lemonthree
  • · Replies 1 ·
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1

Undergrad Decomposition per the Fundamental Theorem of Finite Abelian Groups

  • jstrunk
  • · Replies 13 ·
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13

Graduate Finite non-abelian group of the order pq, pq primes

  • Sportin' Life
  • · Replies 2 ·
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2

-311.1.5.8 Ax=b in parametric vector form,

  • karush
  • · Replies 7 ·
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7

311.1.5.5 homogeneous systems in parametric vector form.

  • karush
  • · Replies 2 ·
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2

Undergrad Prove that dim(V⊗W)=(dim V)(dim W)

  • Karl Karlsson
  • · Replies 2 ·
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2

Undergrad Do Hermitian operator properties change in infinite-dimensional spaces?

  • LCSphysicist
  • · Replies 2 ·
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2

Undergrad Does anyone really understand what's really going on with this video?

  • swampwiz
  • · Replies 7 ·
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7

Undergrad What is the definition of trace for n-indexed tensor in group theory?

  • dontknow
  • · Replies 1 ·
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1

Undergrad Rotational invariance of cross product matrix operator

  • Filip Larsen
  • · Replies 7 ·
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7