linear-algebra

  1. Is the set $\{(x, y) : |y| = |x|\}$ a subspace of $\mathbb{R^2}$?
  2. Matrix problems with unknowns on both sides.

  3. Linear Algebra: Proof Question Concerning Uniqueness of RREF and Use of Fields
  4. Project 3D point onto cylinder

  5. Finding altitude and azimuth with an accelerometer and magnetometer

  6. How Do Integrals Behave In Higher Dimensions?
  7. Proving that proposed vectors actually form a basis for Null space

  8. Is a combination of the vectors in a basis of a space also a basis of that space?
  9. Solve many linear systems of similar structure

  10. Geometric Interpretation of a Matrix Transformation's Eigen Vectors

  11. Give the new basis $(H_k)_{k=0,1,2,3}$ Of $R_3[X]$ to express $P$ by $P(0),P(1),P'(0),P'(1)$
  12. What does it mean to "fix" an orthonormal basis?

  13. How exactly to use Cayley's Hamilton's theorem to find $A^{50}$ in this case? (matrix recursion equation)

  14. Bijection of quadratic forms and symmetric bilinear forms in characteristic $2$
  15. Why is $\operatorname{SO}(p,q)$ isomorphic to $\operatorname{SO}(q,p)$?
  16. Proof of Statistics which makes use of basic linear algebra notions

  17. Absolute Determinant: Geometric Argument
  18. Is there any quick and direct way to find minimal polynomial?

  19. What does cube $[0,1]^{400}$ in Euclidean space refer to?

  20. How to find $\ker(T)$

  21. How to find the sum of all elements of inverse of a matrix without finding the inverse explicitly?

  22. On polynomial long division
  23. Find a unique solution for the Decomposition of two matrices
  24. If $p$, $q$ are two orthogonal projections, then all eigenvalues of $q \circ p$ are in $[0,1]$
  25. Is there any use in expressing a matrix $A$ in terms of the basis of eigenvectors of $A^T A$

  26. Prove that $f$ is nilpotent.

  27. Show $(p_1,p_2,p_3,p_4)$ is linearly independent.
  28. Largest/smallest dimensions possible?

  29. Matrix $-VDV$ is positive semidefinite equivalence

  30. Why $f(z)=\frac{az+b}{cz+d}$, $a,b,c,d \in \mathbb C$, is a linear transformation?

  31. please some help

  32. Invertible Matrix & determinator

  33. Why is the set $\{1,\sqrt {2}\}$ linearly independent over $\mathbb Q$ but not over $\mathbb R$?

  34. Scalar multiplication well-defined using tensor product universal property
  35. How to show $A$ and $P^{-1}BP$ have same minimal polynomial?

  36. Existence of natural symplectomorphism for two structures in $V \times V$.

  37. linear independent functions

  38. Show that $\det(A) = 0$
  39. Weighted Least Squares Estimator Without Intercept

  40. A special case of a nilpotent linear operator

  41. Affine Set Theorem
  42. Solving Ax + Bx = b (same matrix in two equations)

  43. Change of basis between $\mathbb{Q}(\sqrt{2}+ \sqrt{3})$ and $\mathbb{Q}(\sqrt{2}, \sqrt{3}) $
  44. Convex sets. Real Analysis.

  45. Spectrum of doubly stochastic matrices
  46. Prove the Linear Algebra about Matrices
  47. How to get asymptotic solution for vector iteration process as $f^{n+1}=B G B^T f^{n}$?

  48. Showing two definitions of the pseudospectrum are equivalent 2

  49. What is the matrix of $f$ in the canonical bases of the two spaces?

  50. Equivalence of two definitions of polar of polytope

  51. Positive semi definiteness of product of matrices

  52. $8$ linear equations and $9$ unknowns can we solve?
  53. How is a Generator Matrix for a (7, 4) Hamming code created?
  54. Infinity norm quotient

  55. Continuous rotation formula of turning particle

  56. Proof for norm of sum of vectors is less/equal to sum of norm of vectors

  57. Determining if given polynomials form a basis.

  58. Find the matrix of $T(p(t)) = tp'(t)$ with respect to the basis $B = \{1, 1 + t, t^2\}$ of $P_2$.

  59. Subspaces questions
  60. Prove isomorphism in infinite-dim condition

  61. How to choose the starting row when computing the reduced row echelon form?
  62. An inequality regarding pojection
  63. Let A be a real square matrix satisfying $A^5 = 0. $

  64. Proving that $ (A + I)^n=(2^n-1)A + I $
  65. Finding the standard matrix of the transformation, is it unique?
  66. Matrix. Calculation

  67. Generating a $d^{z}$-disjunct binary matrix ($M(m,k,r)$) for group testing/pooling design

  68. For which (c,d) is the transformation linear?

  69. Prove linear transformation is one to one
  70. Linear Operator Example
  71. Eigenvectors corresponding to different eigenvalues of a normal operators are ortogonal

  72. Importance of Decomposing Linear Operators
  73. Given that if a line L is parallel to a plane P, how can I prove that any direction vector for L must be orthogonal to any normal vector for P?
  74. Application of Linear System: Financial Consulting

  75. Linear Algebra-Interpretation of a line in regards to the solutions of the equation

  76. Finding a maximal independent subset given $X$ where $AX=0$.

  77. Orthogonality of vectors that minimize a function on affine spaces

  78. When the Lights Out puzzle vectors over elementary abelian field of dimension $n^2$ form a basis

  79. Finding kernel and range
  80. Proving linear transformation

  81. Similar concentration results to Restricted Isometry Property?

  82. How can vector-tensor product be defined?

  83. Elementary Linear Algebra Matrix Representations

  84. Write trinomials as nonnegative linear combination

  85. Eigenvalue on symmetric matrices inequality

  86. Reference for theorem of least square solutions of linear systems

  87. Direction vector of a line
  88. Finding matrix relative to a polynomial basis and basis in R2?
  89. Expressing a linear combination through row reduction versus expressing it using dot product?
  90. short Linear Algebra / Orthogonality quiz

  91. How to calculate $f(p)_G$ where $p$ is given by$ p(x)=4 x^2+8 x+4 ∀x∈\Bbb R.$?

  92. Determine the $\det(A)$ if $A$ is a eigenvector of a linear operator

  93. Why are elementary row operations useful?

  94. Prove that $\sum_{j=1}^n a_{ij} = \lambda$ is an eigenvalue of $A$.
  95. Finding basis for the dual space

  96. Solve the following nxn determinant by reducing it to a upper/lower triangular determinant

  97. Find out how many invertible and diagonal solutions $X^2-2X=0 $ has when $ X \in\Bbb{R}^{3\times 3}$
  98. Let $T(v_i)=v_i+v_{i-1}$. Find $[T_\beta]$ and $[T_\gamma]$.
  99. How many pages did Henry read in the first day? (Can you show a method?)

  100. How can I prove $AB = BA$