<we><edit> <!-- questions and answers -->
graph-theory
functions
probability-distributions
operator-theory
vector-spaces
differential-equations
algebra-precalculus
contest-math
matrices
exponential-function
euclidean-geometry
proof-verification
recurrence-relations
differential-geometry
definite-integrals
calculus
asymptotics
riemannian-geometry
functional-analysis
field-theory
terminology
algebraic-topology
normal-distribution
polynomials
number-theory
matrices
gradient of logdet of sum of two matrices
matrices
Is the diagonal matrix the only matrix whose square is diagonal?
linear-algebra
matrices
matrix-decomposition
Derivative transpose (follow up)
matrices
derivatives
linear-regression
transpose
solve $\mu\cdot P^6=d$ with $P$ a matrix
matrices
matrix-equations
Eigenvalues of a $3\times3$ matrix: geometric and algebraic multiplicities
linear-algebra
matrices
Loewner partial-order vs. ordering of eigenvalues
linear-algebra
matrices
positive-semidefinite
adjoint of a matrix?
linear-algebra
matrices
Does the algebraic multiplicity of all the eigenvalues of a matrix always add up to the dimension of the matrix?
linear-algebra
matrices
eigenvalues-eigenvectors
If $x^tAx$ = $x^tBx$ for all $x\in R^n$. Then what can I say about the matrices? Are they congruent to each other?
linear-algebra
matrices
quadratic-forms
What are the Rank and Signature of the Matrices whose quadratic forms are $xy+z^2$?
linear-algebra
matrices
vector-spaces
quadratic-forms
Find the precise conditions on $a,b,c$ in order that the matrix $\tiny\begin{bmatrix}a & b\\ c & d\end{bmatrix}$ will be nonnegative definite.
linear-algebra
matrices
numerical-methods
matrix-calculus
LU decomposition on 5 by 3 matrix.
linear-algebra
matrices
matrix-decomposition
Number of n X n binary matrices with every 1 adjacent to some zero and every 0 adjacent to some one, horizontally or vertically.
combinatorics
matrices
binary
Matrix multiplication: interpreting and understanding the process
linear-algebra
matrices
intuition
faq
Given a mapping for $\mathbb R^2 \to \mathbb R^3 , A,$ find new basis for $\mathbb R^2$ and $\mathbb R^3$ such that the mapping is now diagonal
linear-algebra
matrices
change-of-basis
Matrix with only real eigenvalues is similar to upper triangular matrix
linear-algebra
matrices
Getting the relative velocity of an collection of objects vectorised
matrices
vectors
symmetric-matrices
vectorization
Why are Vandermonde matrices invertible?
linear-algebra
matrices
polynomials
Conjugation with Pauli matrices
linear-algebra
matrices
vector-spaces
Properties of upper triangular matrix with complex entries
linear-algebra
matrices
Math grids unique values
matrices
geometry
functions
coloring
Determinant of a block matrix, blocks are transformations of the same matrix
linear-algebra
matrices
Cross product: matrix transformation identity
linear-algebra
matrices
Least square solution based on the pseudoinverse solved efficiently with singular value decomposition
linear-algebra
matrices
least-squares
svd
Deducing Farkas' lemma from its convex hull formulation (full details inside)
linear-algebra
matrices
Atkin-Lehner operator $W_q$
matrices
modular-forms
A conjecture about the eigenvalues of symmetric pentadiagonal Toeplitz matrix
linear-algebra
matrices
eigenvalues-eigenvectors
What are "clockwise" and "counter-clockwise" in matrix rotation?
matrices
rotations
Is $SO(n)$ a normal subgroup of $SO(n+1)$?
matrices
differential-geometry
manifolds
riemannian-geometry
Condition number for a complex square matrix
matrices
numerical-linear-algebra
Is $\mbox{tr}(A^2)$ always nonnegative?
linear-algebra
matrices
trace
Positive semi-definiteness of a matrix implying certain structure
linear-algebra
matrices
positive-semidefinite
How does the following expression scale with respect to $\epsilon$?
linear-algebra
matrices
numerical-methods
numerical-linear-algebra
perturbation-theory
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
linear-algebra
matrices
determinant
Primitive roots of unity occuring as eigenvalues of a product
matrices
eigenvalues-eigenvectors
roots-of-unity
Find shape function for finite element
linear-algebra
matrices
functional-analysis
finite-element-method
Existence of matrix with certain property over a finite field
abstract-algebra
matrices
finite-fields
trace
Prove that $V$ is not a free module.
abstract-algebra
matrices
ring-theory
modules
integral-domain
Prove or disprove $ABA^{T} = AC$ implies $BA^{T} =C$
linear-algebra
matrices
Prove $V$ is a cyclic $F[A]$ module $\iff$ it has the same characteristic and minimal polynomials
linear-algebra
abstract-algebra
matrices
modules
minimal-polynomials
Covering Map $S^3 \to \mathbb{RP}^3$
general-topology
matrices
covering-spaces
The set of matrices of form $A^3+B^3$ with multiplication is a monoid
abstract-algebra
matrices
monoid
Block matrix inversion
matrices
inverse
pseudoinverse
Sum of component projection matrices
linear-algebra
matrices
regression
Can you determine from the minors if the presented module is free?
linear-algebra
matrices
commutative-algebra
Given invertible matrices A,B and P, we say that A is right equivalent to B if A = BP. Show that right equivalence is an equivalence relation.
matrices
equivalence-relations
Canonical base of polynomial (Linear Algebra)
linear-algebra
matrices
polynomials
How to find the basis for the eigenspace if the rref form of λI - A is the zero vector?
linear-algebra
matrices
eigenvalues-eigenvectors
Conditions on coefficients of positive semidefinite matrix with certain symmetries
matrices
inequality
eigenvalues-eigenvectors
matrix-equations
positive-semidefinite
What are the main uses of the LU decomposition?
linear-algebra
matrices
Find a Matrix with a given null space
linear-algebra
matrices
eigenvalues-eigenvectors
matrix-rank
why what number goes where in the matrix when given the linear transformation and basis
matrices
linear-transformations
Determine whether or not the modules over $R=\mathbb{C}[x,y]$ presented by the following matrices are free
abstract-algebra
matrices
polynomials
ring-theory
modules
What is the maximum number of objects that can fit in a NxN matrix without overlapping?
matrices
discrete-mathematics
Determinant of a finite-dimensional matrix in terms of trace
linear-algebra
matrices
determinant
trace
how to show these two matrices commutes
matrices
Solving for Unknown in Matrix
matrices
eigenvalues-eigenvectors
diagonalization
transpose
2 $\times$ 2 Symmetry matrices of a square
matrices
group-theory
symmetry
Rank of Matrix and dimension of the image of the function corresponding with that matrix
linear-algebra
matrices
vector-spaces
linear-transformations
Derivative of tr( A^T B C ) w.r.t. C
linear-algebra
matrices
derivatives
partial-derivative
Derivative of a matrix AXBX
matrices
derivatives
matrix-calculus
Prove the $\ell^2$ norm of a linear transformation $A: \mathbb{R}^n \to \mathbb R^n$ is the maximum eigenvalue
real-analysis
matrices
eigenvalues-eigenvectors
norm
Have you seen this “exponent of matrices” before?
linear-algebra
matrices
numerical-linear-algebra
How to diagonalize matrices with repeated eigenvalues?
linear-algebra
matrices
eigenvalues-eigenvectors
diagonalization
What are the "fancy linear-algebra methods" that would allow me to solve this physics problem without Kirchhoff's Rule?
linear-algebra
matrices
physics
eigenvector of compositions implies eigenvector of respective functions in composition?
linear-algebra
matrices
eigenvalues-eigenvectors
linear-transformations
eigenfunctions
What set of properties does a matrix have to have in order for all its pairs of distinct eigenvectors $x$ and $y$ to have $x^Ty=0?$
linear-algebra
matrices
covariance
Finding The Characteristic Polynomial of a Matrix With Integer Sum Coefficients.
linear-algebra
matrices
determinant
cayley-hamilton
$A$ is positive definite iff there exists a nonsingular $C$ s.t. $C^*AC$ is positive definite
linear-algebra
matrices
positive-definite
How does Schur Complement aid in solving Linear Least Squares Problem
matrices
matrix-decomposition
least-squares
Show that λ +c is an eigenvalue of B
matrices
proof-writing
eigenvalues-eigenvectors
Matrix multiplication to show that $A \cdot B = C$
matrices
proof-verification
matrix-equations
matrix-decomposition
determinant of a standard magic square
linear-algebra
matrices
determinant
magic-square
Prove that $\|\mathbf{X}\|_\sigma \leq \sqrt{rank(X)} \|\mathbf{X}\|_F$
linear-algebra
matrices
inequality
norm
matrix-rank
Vector whose inner product is positive with every vector in given basis of $\mathbb{R}^n$
linear-algebra
matrices
bilinear-form
Linear Algebra Invertible Matrix Theorem Proof
linear-algebra
matrices
linear-transformations
How to differentiate an expression with respect to a symmetric matrix?
matrices
derivatives
partial-derivative
symmetric-matrices
Properties of $A^TA$ transformation
linear-algebra
matrices
orthogonality
Solution of linear system
linear-algebra
matrices
For every real matrix $A$ there is a non-negative vector $v$ with $Av \geq A^Tv$ coordinate-wise.
linear-algebra
matrices
Calculate the image and a basis of the image (matrix)
linear-algebra
matrices
vector-spaces
How and the best way to resolve this matrix equation
matrices
matrix-equations
Find the Determinant of the given Matrix
linear-algebra
matrices
determinant
A real symmetric matrix decomposed by diagonal entries
real-analysis
linear-algebra
matrices
Derivative of $\ \ Trace(GG^T GG^T)\ \ $ with respect to G
matrices
derivatives
positive definite matrix as a matrix blocks
matrices
positive-semidefinite
Complete Pivoting VS Partial Pivoting in Gauss Elimination
linear-algebra
matrices
numerical-methods
gaussian-elimination
how to prove for any linear transformation form $R_n$ to$R_m$ ,there is an orthonormal basis such that $T(u_i)*T(u_j) = 0$ if $i \neq j$
linear-algebra
matrices
Counting matrices over a finite field.
combinatorics
matrices
finite-fields
True/False From Howard Anton's Linear Algebra
linear-algebra
matrices
determinant
To show that $0$ is an eigenvalue of $A$, with multiplicity at least $r − 1$.
matrices
graph-theory
How many solutions do these systems of equations have?
linear-algebra
matrices
systems-of-equations
When and why attached vector is ambiguously defined?
linear-algebra
matrices
jordan-normal-form
Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$
linear-algebra
matrices
binomial-coefficients
Matrix inverse, Schur's complement and the chicken or the egg dilemma
matrices
matrix-calculus
inverse-function
The linear operator $T_A(B)=AB-BA$ defined on $\mathbb M_n(\mathbb C)$ has a null determinant
linear-algebra
matrices
proof-verification
determinant
Let $T : R^2 → R^3$ be the linear transformation given by a rule Find the matrix $A$ that represents $T$ relative to ordered bases
matrices
Generate Multivariate normal matrix using cholesky issue with accuracy
matrices
multivariable-calculus
matrix-decomposition
Prove that nuclear norm of a matrix is equal to the sum of squares of Frobenius norm
linear-algebra
matrices
norm
matrix-decomposition
matrix elementary column operations
linear-algebra
matrices
vectors
laplace-transform
gaussian-elimination