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  • linear algebra - Rank of sum of rank-$1$ matrices - Mathematics Stack . . .
    linear-algebra matrices matrix-rank rank-1-matrices Share Cite edited Jul 1, 2023 at 19:18 Rodrigo de Azevedo 24 8k 7 52 122 asked Mar 10, 2014 at 20:36
  • Proof verification: Prove that a tree with n vertices has n-1 edges
    What you are fundamentally saying is that if you have a tree with n vertex and n-1 edges, you can obtain a tree with n+1 vertices and n edges You can add the new edge to any of the previous vertex, but how you didn't prove that doing this way you'll exhaust all the trees with n+1 vertices
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    B站UP主北美运动学博士Bruce_PhD经良子本人同意，公开并解读了良子最新的体检报告
  • linear algebra - Showing that $l_2$ norm is smaller than $l_1 . . .
    Yes And thanks for reaching out and asking It is the Minkowshi inequality under repeated use, where the measure employed is the counting measure Here is the idea: The M inequality says that ∥f + g∥ ≤ ∥f∥ + ∥g∥ ‖ f + g ‖ ≤ ‖ f ‖ + ‖ g ‖ $\Vert f+g\Vert \le \Vert f\Vert +\Vert g\Vert$ So if we apply it multiple times we can see that ∥f + g + h∥ ≤ ∥f + g∥
  • Inverse of the sum of matrices - Mathematics Stack Exchange
    The technique is useful in computation, because if the values in A and B can be very different in size then calculating 1 A+B 1 A + B $\frac{1}{A+B}$ according to (3) (3)
  • Simplify K! (K+1)! - Mathematics Stack Exchange
    Pretend K=3 That means (K+1)= 4 This means you'd be dividing 3*2*1 by 4*3*2*1 Consider how you'd cancel out multiples by dividing them Like how (2 (5+x)) 2 would just equal 5+x Following that idea we'd pretty much be able to cancel out every number in the numerator, so long as its also in the denominator This would end up canceling every number except for 4 which equals (K+1) Essentially
  • Show that the eigenvalues of a unitary matrix have modulus $1$
    However, an interesting thing is that you can perhaps stop at the third last step, because an equivalent condition of a unitary matrix is that its eigenvector lies on the unit circle, so therefore, has magnitude 1
  • Taylor series of $\\sqrt{1+x}$ using sigma notation
    Taylor series of 1 + x− −−−−√ 1 + x $\sqrt{1+x}$ using sigma notation Ask Question Asked 12 years, 6 months ago Modified 5 years, 4 months ago
  • Why Markov matrices always have 1 as an eigenvalue
    qp=q where p is prob state transition matrix this means Y = 1 as an eigen vector of P' which also means There is an unique probability vector q which is an eigenvector associated with eigenvalue 1





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