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How can I prove using induction that the Hadamard matrices are orthogonal?

score 1.8k · Answer 1 · 2026-04-09 20:59:21

1.8k

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How can I prove using induction that the Hadamard matrices are orthogonal?

Published on 09 Apr 2026 - 20:59

score 85 · Answer 2 · 2026-04-09 03:00:29

85

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context-free languages operation closure

Published on 09 Apr 2026 - 3:00

score 69 · Answer 3 · 2026-04-16 00:28:56

69

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Prove by induction $n^{1/n} ≤ \frac{n+1}{2}$

Published on 16 Apr 2026 - 0:28

score 1k · Answer 4 · 2026-04-28 20:08:18

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Solution verification: Prove by induction that $a_1 = \sqrt{2} , a_{n+1} = \sqrt{2 + a_n} $ is increasing and bounded by $2$

Published on 28 Apr 2026 - 20:08

score 127 · Answer 5 · 2026-04-12 08:25:36

127

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How to prove $ \sum\limits_{k=1}^{n}\frac{k}{(k+1)!}=1-\frac{1}{(n+1)!}$ using induction?

Published on 12 Apr 2026 - 8:25

score 3.6k · Answer 6 · 2026-04-15 13:04:01

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Why are two base cases needed to prove that $n<2^n$ for all $n\geq 0\,$?

Published on 15 Apr 2026 - 13:04

score 624 · Answer 7 · 2026-04-17 12:20:26

624

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Proving by induction on the number of vertices that: every acyclic simple graph is bipartite

Published on 17 Apr 2026 - 12:20

score 108 · Answer 8 · 2026-04-11 01:02:30

108

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How to perform induction step in this question?

Published on 11 Apr 2026 - 1:02

score 1k · Answer 9 · 2026-04-12 20:00:06

1k

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Nim Variant - Strong Induction Proof

Published on 12 Apr 2026 - 20:00

score 27 · Answer 10 · 2026-04-11 22:10:52

27

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How to go about induction that deals with inequalitites

Published on 11 Apr 2026 - 22:10

score 90 · Answer 11 · 2026-04-14 21:28:17

90

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Find a formula for $ 1\times3^0 + 3\times3^1 + 5\times3^2 + ... +(2n+1)\times3^n$.

Published on 14 Apr 2026 - 21:28

score 114 · Answer 12 · 2026-04-16 14:33:20

114

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Prove that if $p \mid a_1a_2 \ldots a_n$, then $p \mid a_j$ for some $j$ with $1 \le j \le n$

Published on 16 Apr 2026 - 14:33

score 1.2k · Answer 13 · 2026-04-16 15:15:42

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Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction

Published on 16 Apr 2026 - 15:15

score 134 · Answer 14 · 2026-04-13 02:43:15

134

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Construction of Natural Numbers

Published on 13 Apr 2026 - 2:43

score 246 · Answer 15 · 2026-04-13 00:49:00

246

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Rewrite $\sum_{i=0}^{n-1} (2i+1)=n^2$ to start induction from $k = 0$?

Published on 13 Apr 2026 - 0:49

List Question

How can I prove using induction that the Hadamard matrices are orthogonal?

context-free languages operation closure

Prove by induction $n^{1/n} ≤ \frac{n+1}{2}$

Solution verification: Prove by induction that $a_1 = \sqrt{2} , a_{n+1} = \sqrt{2 + a_n} $ is increasing and bounded by $2$

How to prove $ \sum\limits_{k=1}^{n}\frac{k}{(k+1)!}=1-\frac{1}{(n+1)!}$ using induction?

Why are two base cases needed to prove that $n<2^n$ for all $n\geq 0\,$?

Proving by induction on the number of vertices that: every acyclic simple graph is bipartite

How to perform induction step in this question?

Nim Variant - Strong Induction Proof

How to go about induction that deals with inequalitites

Find a formula for $ 1\times3^0 + 3\times3^1 + 5\times3^2 + ... +(2n+1)\times3^n$.

Prove that if $p \mid a_1a_2 \ldots a_n$, then $p \mid a_j$ for some $j$ with $1 \le j \le n$

Proving $\sqrt{1+\sqrt{2+\cdots+\sqrt{n}}} < 3$ for $n\geq 1$ by induction

Construction of Natural Numbers

Rewrite $\sum_{i=0}^{n-1} (2i+1)=n^2$ to start induction from $k = 0$?

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