matrices

  1. Diagonally Dominant Matrix Preserved after Gaussian Elimination (with a modification)

  2. how to reduce a vector to a scalar?

  3. Find the closest point ax to b

  4. Is it possible to construct eigenvalues and eigenvectors of Hamiltonian based on its subspaces?

  5. A problem on rank of a matrix over two fields
  6. Matrix Products with Angles

  7. Is null vector always linearly dependent?
  8. Show the sequence $\vec{x_k}= \lambda_1^{-k}A^k\vec{x}$ converges to eigenvector $\vec{y}$ with eigenvalue $\lambda_1$
  9. how to show existance of such a matrix

  10. How to show that $M$ is nonsingular (iff $A-BC$ = nonsingular)$\begin{bmatrix}A&B\\C&I\\\end{bmatrix}$

  11. Finding the eigenvector of a matrix using another matrix

  12. If $Ax=0$ has infinitely many solutions, does $A^Tx=b$ also have infinitely many solutions?
  13. What’s the volume of the hyperbolic truncated simplex
  14. The Spectral Theorem

  15. Factorization of singular matrix

  16. How to prove this matrices question?
  17. min-plus problem complexity time

  18. Generating primes from other primes
  19. Why does Friedberg say that the role of the determinant is less central than in former times?

  20. Rotation-invariant matrix operations, like Frobenius inner product?

  21. Transformation Representation on 2 basis
  22. Determinant for equivalent matrices?
  23. Numerical range of normal matrices

  24. How to calculate a matrix $M$ by dividing 2 vectors?

  25. What is the matrix representation of Radon transform?
  26. What are some mathematically interesting computations involving matrices?

  27. Optimal Matching Distance
  28. Get $A$ and $C$ matrix from Observability matrix
  29. Whether range of matrix $A^TA$ is the same as that of $A^T$
  30. Sufficient condition for the block matrix $\big(\begin{smallmatrix} B & A^T \\ A & 0 \end{smallmatrix} \big)$ to be invertible

  31. Eigenvalues of same-row matrices
  32. Ax=0, why A must be singular matrix for having x different from 0?
  33. Let $A$ be an $n \times n$ matrix. If every non-zero vector $v$ is an evector of $A$, prove that $A$ is a diagonal matrix

  34. Second Derivative of a Determinant
  35. Logarithm of a matrix $A \in M_2 (\mathbb{C})$
  36. Sum of squares of minors of orthogonal matrix

  37. Let A be an $m \times n$ matrix, using matrix algebra prove that

  38. Factorizing a matrix into a matrix and its transpose

  39. Arbitrary non-integer power of a matrix

  40. If $A=\left(\begin{array}{cc} 2 & 1\\ 1 & 3 \end{array}\right)$, find $\cos\left(\frac{A\pi}{6}\right)$

  41. Show that $ trace(AB) = (\sum_{i=1}^{n} a_{i}b_{i})^2 $

  42. Why is this inequality about norm of the inverse of a nonsingular matrix holds?
  43. Find $A^n$, if $n$ is Natural number

  44. Do Diagonal Matrices Always Commute?
  45. Find all matrices [3x3] that commute with given matrix

  46. Creating a monotone matrix from a given matrix

  47. Why dont we use Given's method to reduce a symmetric matrix to diagonal form rather than tridiagonal form, and why is tridiagonal form desirable?
  48. Question about the following vector belongs to the range space of the linear operator or not?
  49. Reference for Kalman-Ho-Narendra Theorem

  50. Transition "political" matrix with an unkown, how to determine its value?

  51. Is the product of a positive definite matrix with it's inverse diagonal diagonalizable?
  52. ${A_1}^k + {A_2}^k + \cdots +{A_n}^k = 0$ for all $k \in \mathbb N_{>0}$ $\implies$ $A_i$ are all nilpotent.
  53. Higher powers of matrix

  54. Inverse of a Particular Matrix help R-{0}

  55. Properties of poset of nonvanishing minors of a matrix

  56. Find the spectral decomposition of $A$
  57. How does the SVD solve the least squares problem?

  58. The basis for the row space for a matrix
  59. Why multiply a matrix with its transpose?
  60. Le A be an n x n matrix. Prove that A is non-singular if and only if rank(A) = n

  61. Projection matrices onto a subspace

  62. Finding the basic and free variables of this matrix

  63. Fifth power of a $2 \times 2$ matrix equal to the multiplicative identity
  64. Determinant of submatrix

  65. 'foreach' Function In Mathmatics

  66. What does adding between dimensions mean if anything at all? Are there useful conventions for doing so?
  67. Fast(est) and intuitive ways to look at matrix multiplication?
  68. Minimal polynomial of matrix with rank 1

  69. Solving simplex using matrix algebra involving artificial variables and surplus variables.

  70. compressive sensing
  71. Doolittle transformation is non-unique for singular matrices
  72. Existence of matrix with $d_{ii} \in \{1,-1\}$ in QR decomposition

  73. Hessian of non-linear quadratic form

  74. Show that every integer eigenvalue of $A$ divides the determinant of $A$.
  75. Diagonal elements of a matrix.

  76. How to partially eliminate an unknown term from a matrix
  77. When a solution of the Sylvester equation is not singular?
  78. Product between a column vector and a row vector
  79. Collecting vector q in $Aq+qB$ with A and B matrices?

  80. I am not finding all the eigenvectors for an eigenvalue
  81. Does $x^T |A| x \geq 0 $ hold?
  82. Inverse of a matrix exponential

  83. Demonstrate using determinant properties that the determinant of $A$ is equal to $2abc(a+b+c)^3$
  84. Matrix Equation $ AXB = (B A)^2$

  85. linear algebra - find x

  86. A surprising result about the product of Blaschke matrices

  87. Bandmatrix number of nonzero elements
  88. $A^3\cdot B^3=X^3+Y^3$.

  89. Derive formula for number of tilings of an $m \times n$ board.

  90. Eigenvalue with largest imaginary part

  91. Find necessary and sufficient conditions for the system of inequalities to have solutions $x$ satisfying...

  92. Find the matrix $Y\in \mathbb{C}^{n \times p} (p <n)$

  93. If $A \in \mathbb{M}_{n\times n}(\mathbb{R})$ with $n\ge 2$ has rank $1$
  94. $A^TA$ is non-singular if and only if $A$ has full row rank

  95. For the $3\times 3$ matrix $A$ with eigenvalues $x_1$, $x_2$, $x_3$ find idempotents matrix $E_1,E_2.E_3$ so that $A=x_1E_1+x_2E_2+x_3E_3$ .
  96. Show that $E_{ij}ME_{kl}= m_{kj}E_{il}$ in $V=M_{2x2}^R$

  97. Find a skew Hilbert-Schmidt operator $S$ such that $a+bS$ is invertible.

  98. Complete the matrix through a rank-one approximation.

  99. Writing entries of sum of matrix row outer products in matrix notation
  100. How can I divide array into blocks?