linear-algebra

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

  2. Finding Eigenvectors [Confused]
  3. Find the closest point ax to b

  4. A problem on rank of a matrix over two fields

  5. Shooting tangent to a moving circle
  6. linear algebra, inner product spaces.
  7. Difference between epimorphism, isomorphism, endomorphism and automorphism Linear transformations with examples

  8. proof linear transformation injective, surjective, isomorphism
  9. How can we extend a base of a vector space to a base of a larger vector space?

  10. Given the transformation matrix, show that $f$ is surjective.

  11. Linear algebra proof on orthogonal diagonalization
  12. Can I solve other recurrence relations with linear algebra than just Fibonacci sequence?

  13. Are there any applications of Algebraic Graph Theory to Computer Science?

  14. From correlated random variables to uncorrelated random variables

  15. Ways to find the orthogonal projection matrix

  16. Linear algebra problem relating to normal equations for linear model with linear constraints

  17. Why Singular Value Decomposition(SVD) has this specific form...

  18. Is null vector always linearly dependent?

  19. Does the image of A equal to the image of the transpose of A

  20. Intersection of two polynomial subspaces

  21. Show the sequence $\vec{x_k}= \lambda_1^{-k}A^k\vec{x}$ converges to eigenvector $\vec{y}$ with eigenvalue $\lambda_1$

  22. Quadratic Diophantine equation - Find all integer solutions

  23. Is there any relation between weights in the eigenvector (corresponding to least eigenvalue) and the columns of a correlation matrix?

  24. Why is the algebra product $A\otimes A\to A$ well defined, given that we know the product $A\times A\to A$?

  25. General partial fraction decomposition

  26. Using multiple independent Vector Spaces to represent a function
  27. how to show existance of such a matrix

  28. Finding the general equation of a cross section of a roof and the position of each joist that makes up its surface

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

  31. What are Pauli matrices?
  32. Finding the eigenvector of a matrix using another matrix

  33. A good Linear Algebra Book for Someone with a rigorous background in it?
  34. The number of invertible linear transformations.

  35. Properties of cross product in $\mathbb{R^3}$

  36. transform matrix to have orthogonal columns

  37. linear algebra: if $A$ is in span $B $ is span $A$ in span $B$
  38. The Spectral Theorem

  39. How to prove this matrices question?

  40. Solving sparse least squares system with limited memory

  41. Extrapolating dimension

  42. It's enough for say that does not exist $Span(S∪T)=Span(S)⨁Span(T)$?
  43. Linear transformations and linear independence
  44. Why does Friedberg say that the role of the determinant is less central than in former times?
  45. Difference between matrix and linear operator

  46. Eigenvalues problem 1

  47. Separation of variable: $f(x)=g(y)$ for all $x,y$ implies $f(x)=g(y)=$ constant, and the constant being eigenvalue

  48. Transformation matrix - Are the matrices correct?

  49. Proving Group Homomorphism between subgroups
  50. Relationship of norm and quadratic form for an ordering
  51. What is a necessary condition to form a set of basis?

  52. Exercises in Sterling K. Berberian's Linear Algebra

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

  54. Transformation Representation on 2 basis
  55. Determinant for equivalent matrices?

  56. How to find distance between vector and a subspace?
  57. Numerical range of normal matrices

  58. Injection from dual space into double dual space

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

  60. Is there connection between Stieltjes transformation and Cauchy integral formula?

  61. Derivative of an L1 norm of transform of a vector.
  62. What is the basis of the vectors contained in the basis of a vector space?
  63. $\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
  64. Proving that a system of $m$ homogeneous linear equations in $n$ variables has a solution in which not all $x_i=0$ if $n>m$

  65. Calculating constant
  66. What are some mathematically interesting computations involving matrices?

  67. Optimal Matching Distance

  68. Whether range of matrix $A^TA$ is the same as that of $A^T$

  69. Sufficient condition for the block matrix $\big(\begin{smallmatrix} B & A^T \\ A & 0 \end{smallmatrix} \big)$ to be invertible

  70. Linear independency in cartesian product of $\mathbb{R}$

  71. If A is a symmetric $n\times n$ matrix, prove that the eigenvectors associated to distinct eigenvalues are orthogonal
  72. Eigenvalues of same-row matrices
  73. $Ax=b$ is solvable, then it has the same solutions of $A^TAx=A^Tb$

  74. Approximation using a matrix

  75. Orthonormal vectors of $\left(-\frac{3+i}{2}, 1\right)$ and $\left(\frac{3+i}{5}, 1\right)$?
  76. If X is isotropic random vector, then is the centered random vector X - E[X] also an isotropic random vector?

  77. Ax=0, why A must be singular matrix for having x different from 0?
  78. spin projector in inverted matrix

  79. 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
  80. Second Derivative of a Determinant

  81. Additive commutator transformation

  82. Sum of squares of minors of orthogonal matrix

  83. Vector question

  84. Direct sum - linear combination (proof verification)
  85. Differential equations 3 points need answer

  86. Let A be an $m \times n$ matrix, using matrix algebra prove that
  87. Show linear independence of $\{1, \cos x, \sin x\}$

  88. Find the Change of Basis Matrix
  89. What does "basis transformation" mean in this context (linear regression using higher order functions)?

  90. Factorizing a matrix into a matrix and its transpose

  91. Finding points on two linear lines which are a particular distance apart
  92. Plane orthogonal to the x-axis
  93. Proof of the unicity of a linear combination

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

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

  96. Why is this inequality about norm of the inverse of a nonsingular matrix holds?
  97. Understanding Vector Spaces

  98. Find $A^n$, if $n$ is Natural number
  99. Do Diagonal Matrices Always Commute?

  100. Prove functions are positive define kernel