matrices

  1. gradient of logdet of sum of two matrices

  2. Is the diagonal matrix the only matrix whose square is diagonal?

  3. Derivative transpose (follow up)
  4. solve $\mu\cdot P^6=d$ with $P$ a matrix
  5. Eigenvalues of a $3\times3$ matrix: geometric and algebraic multiplicities

  6. Loewner partial-order vs. ordering of eigenvalues
  7. adjoint of a matrix?
  8. Does the algebraic multiplicity of all the eigenvalues of a matrix always add up to the dimension of the matrix?
  9. 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?

  10. What are the Rank and Signature of the Matrices whose quadratic forms are $xy+z^2$?
  11. 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.

  12. LU decomposition on 5 by 3 matrix.

  13. Number of n X n binary matrices with every 1 adjacent to some zero and every 0 adjacent to some one, horizontally or vertically.

  14. Matrix multiplication: interpreting and understanding the process
  15. 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

  16. Matrix with only real eigenvalues is similar to upper triangular matrix

  17. Getting the relative velocity of an collection of objects vectorised
  18. Why are Vandermonde matrices invertible?

  19. Conjugation with Pauli matrices

  20. Properties of upper triangular matrix with complex entries
  21. Math grids unique values
  22. Determinant of a block matrix, blocks are transformations of the same matrix
  23. Cross product: matrix transformation identity
  24. Least square solution based on the pseudoinverse solved efficiently with singular value decomposition

  25. Deducing Farkas' lemma from its convex hull formulation (full details inside)
  26. Atkin-Lehner operator $W_q$

  27. A conjecture about the eigenvalues of symmetric pentadiagonal Toeplitz matrix

  28. What are "clockwise" and "counter-clockwise" in matrix rotation?
  29. Is $SO(n)$ a normal subgroup of $SO(n+1)$?
  30. Condition number for a complex square matrix

  31. Is $\mbox{tr}(A^2)$ always nonnegative?

  32. Positive semi-definiteness of a matrix implying certain structure
  33. How does the following expression scale with respect to $\epsilon$?

  34. $\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$

  35. Primitive roots of unity occuring as eigenvalues of a product

  36. Find shape function for finite element

  37. Existence of matrix with certain property over a finite field

  38. Prove that $V$ is not a free module.

  39. Prove or disprove $ABA^{T} = AC$ implies $BA^{T} =C$

  40. Prove $V$ is a cyclic $F[A]$ module $\iff$ it has the same characteristic and minimal polynomials

  41. Covering Map $S^3 \to \mathbb{RP}^3$
  42. The set of matrices of form $A^3+B^3$ with multiplication is a monoid

  43. Block matrix inversion

  44. Sum of component projection matrices

  45. Can you determine from the minors if the presented module is free?

  46. 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.
  47. Canonical base of polynomial (Linear Algebra)

  48. How to find the basis for the eigenspace if the rref form of λI - A is the zero vector?
  49. Conditions on coefficients of positive semidefinite matrix with certain symmetries

  50. What are the main uses of the LU decomposition?
  51. Find a Matrix with a given null space
  52. why what number goes where in the matrix when given the linear transformation and basis
  53. Determine whether or not the modules over $R=\mathbb{C}[x,y]$ presented by the following matrices are free

  54. What is the maximum number of objects that can fit in a NxN matrix without overlapping?

  55. Determinant of a finite-dimensional matrix in terms of trace

  56. how to show these two matrices commutes

  57. Solving for Unknown in Matrix
  58. 2 $\times$ 2 Symmetry matrices of a square
  59. Rank of Matrix and dimension of the image of the function corresponding with that matrix
  60. Derivative of tr( A^T B C ) w.r.t. C

  61. Derivative of a matrix AXBX
  62. Prove the $\ell^2$ norm of a linear transformation $A: \mathbb{R}^n \to \mathbb R^n$ is the maximum eigenvalue

  63. Have you seen this “exponent of matrices” before?

  64. How to diagonalize matrices with repeated eigenvalues?

  65. What are the "fancy linear-algebra methods" that would allow me to solve this physics problem without Kirchhoff's Rule?

  66. eigenvector of compositions implies eigenvector of respective functions in composition?
  67. What set of properties does a matrix have to have in order for all its pairs of distinct eigenvectors $x$ and $y$ to have $x^Ty=0?$
  68. Finding The Characteristic Polynomial of a Matrix With Integer Sum Coefficients.

  69. $A$ is positive definite iff there exists a nonsingular $C$ s.t. $C^*AC$ is positive definite
  70. How does Schur Complement aid in solving Linear Least Squares Problem
  71. Show that λ +c is an eigenvalue of B
  72. Matrix multiplication to show that $A \cdot B = C$
  73. determinant of a standard magic square

  74. Prove that $\|\mathbf{X}\|_\sigma \leq \sqrt{rank(X)} \|\mathbf{X}\|_F$

  75. Vector whose inner product is positive with every vector in given basis of $\mathbb{R}^n$

  76. Linear Algebra Invertible Matrix Theorem Proof

  77. How to differentiate an expression with respect to a symmetric matrix?
  78. Properties of $A^TA$ transformation

  79. Solution of linear system

  80. For every real matrix $A$ there is a non-negative vector $v$ with $Av \geq A^Tv$ coordinate-wise.
  81. Calculate the image and a basis of the image (matrix)

  82. How and the best way to resolve this matrix equation

  83. Find the Determinant of the given Matrix

  84. A real symmetric matrix decomposed by diagonal entries
  85. Derivative of $\ \ Trace(GG^T GG^T)\ \ $ with respect to G
  86. positive definite matrix as a matrix blocks
  87. Complete Pivoting VS Partial Pivoting in Gauss Elimination
  88. 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 $i \neq j$

  89. Counting matrices over a finite field.

  90. True/False From Howard Anton's Linear Algebra

  91. To show that $0$ is an eigenvalue of $A$, with multiplicity at least $r − 1$.
  92. How many solutions do these systems of equations have?

  93. When and why attached vector is ambiguously defined?

  94. Inverse of the $n$-by-$n$ matrix $(a_{jk})$ where $a_{jk} = \binom{j-1}{k-1}$
  95. Matrix inverse, Schur's complement and the chicken or the egg dilemma

  96. The linear operator $T_A(B)=AB-BA$ defined on $\mathbb M_n(\mathbb C)$ has a null determinant
  97. 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

  98. Generate Multivariate normal matrix using cholesky issue with accuracy
  99. Prove that nuclear norm of a matrix is equal to the sum of squares of Frobenius norm
  100. matrix elementary column operations