Beyond Infinity

 3 Why does an affine transformation $A$ when constrained by $A^TA=\lambda^2I$ result in a similarity transformation? 1 Eigen-Decomposition of Householder operator 1 logic formalizing: The multiplication of every two positive numbers is also positive 1 Sum of subspaces equal to span of union of subspaces 1 Prove by induction. Show that if $n ≥ 6$, then $n! > n^3$

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### Question (1)

 0 Is sum of vector subspaces analogous to union of subsets?

### Tags (25)

 6 linear-algebra × 6 1 vector-spaces 4 matrices × 3 1 rational-numbers 3 linear-transformations 1 sequences-and-series 1 logic × 2 1 irrational-numbers 1 solution-verification × 2 1 number-theory

### Bookmarks (16)

 111 Convergence of $\sum_{n=1}^{\infty} \frac{\sin(n!)}{n}$ 101 Can we remove any prime number with this strange process? 8 Are the numbers $\sqrt{n^2 + q^2}$, $n=0,1,\dots$, linearly dependent over $\mathbb{Q}$? 3 Deletion of given matrix entry via matrix product 3 $x^{x^{1/x}}$ has the same first $\lfloor x \rfloor$ decimals as the number $3\sqrt{\lfloor x\rfloor}$ when $x=\pi$ and $x=e$. Why? Are there others? [closed]

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