Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Sign up for free
Menu
Search
Features
All features
Private URLs
Password Protection
Custom URLS
Scheduled publishing
Remove Branding
Restrict embedding
Deck Collections
Notes
Features
All features
Private URLs
Password Protection
Custom URLS
Scheduled publishing
Remove Branding
Restrict embedding
Deck Collections
Notes
Explore
Featured decks
Featured speakers
Programming
Technology
Storyboards
Explore
Featured decks
Featured speakers
Programming
Technology
Storyboards
Pricing
Search
Sign in
Sign up for free
linear-algebra-in-n-minutes
Search
hama_du
September 21, 2015
Science
260
0
Share
Embed
Copy iframe code
Copy JS code
Copy link
Start on current slide
linear-algebra-in-n-minutes
某所での勉強会の発表資料。厳密性や計算方法は彼方に放り投げた
しゃべりでの補完が多いのでスライドだけだと説明不足かも
hama_du
September 21, 2015
More Decks by hama_du
See All by hama_du
Google File System
hamadu
0
97
Distinct Query using HyperLogLog
hamadu
2
91
木の上を歩こう
hamadu
1
1.1k
Other Decks in Science
See All in Science
Toward Causal Scientific Discovery with AI
sshimizu2006
0
210
白金鉱業Meetup Vol.25 【初学者向け発表枠】「で、この施策って効いてるの」に答える効果検証の基礎 ~ATE / ATT / CATE / LATEを現場の問いに翻訳する~
brainpadpr
1
340
明治薬科大学講義_ビッグデータ解析を支えるデータベース技術とクラウドコンピューティング
ktatsuya
1
200
HOLO: Homography-Guided Pose Estimator Network for Fine-Grained Visual Localization on SD Maps
tomoaki0705
0
160
Conwayの法則を"ちゃんと"使うために — 原典でConwayは何を言っていたのか
bonotake
10
7.4k
言葉をはかる:テキストマイニング入門①講義編
satocos135
0
270
ssmonline #51 ヤマサキ春のサメ祭り 2026 / ssmjp Yamasaki Spring JAWS Festival 2026
naospon
1
160
(CVPR2026) Back to Basics: Let Denoising Generative Models Denoise
shumpei777
0
400
バランスって大事だね
akasan
1
160
機械学習 - K-means & 階層的クラスタリング
trycycle
PRO
0
2.2k
O(log n)-Approximation Algorithms for Bipartiteness Ratio
tasusu
0
260
大黒市で発生した大規模インシデント の ポストモーテムから読み解く、 記憶媒体消去の大切さ
shucho0103
0
290
Featured
See All Featured
Designing for Timeless Needs
cassininazir
1
520
Statistics for Hackers
jakevdp
799
230k
From Legacy to Launchpad: Building Startup-Ready Communities
dugsong
0
350
How Software Deployment tools have changed in the past 20 years
geshan
2
35k
Building Applications with DynamoDB
mza
96
7.2k
Redefining SEO in the New Era of Traffic Generation
szymonslowik
1
460
SEOcharity - Dark patterns in SEO and UX: How to avoid them and build a more ethical web
sarafernandez
0
300
Measuring & Analyzing Core Web Vitals
bluesmoon
9
1k
How Fast Is Fast Enough? [PerfNow 2025]
tammyeverts
3
920
So, you think you're a good person
axbom
PRO
2
2.2k
Designing Dashboards & Data Visualisations in Web Apps
destraynor
232
55k
Cheating the UX When There Is Nothing More to Optimize - PixelPioneers
stephaniewalter
287
14k
Transcript
/Ͱ͔ͬͨؾʹͳΔ ઢܗೖ
͓͠ͳ͕͖ w ߦྻͷ֓೦ w ߦྻͷ͠ࢉɺఆഒɺֻ͚ࢉ w ߦྻͱϕΫτϧ w ݻ༗ͱݻ༗ϕΫτϧ w
ߦྻͷ/
͜ͷࢿྉ͕Χόʔ͠ͳ͍ൣғ w ߦྻࣜ w ˠຊݻ༗ͷܭࢉʹߦྻ͕ࣜඞཁʹͳΔͷͰ͕͢ɺ࣌ ؒͷ߹্ল͍͍ͯ·͢ɻ w /࣍ݩ ࣍ݩҎ্ ͷઢܗมʹؔ͢Δٞ
w ˠߦྻͷϥϯΫͱ͔*Nͱ͔,FSͱ͔ w ݫີͳূ໌ w ˠઢܗͷڭՊॻΛಡΜͰ͍ͩ͘͞ɻ
ߦྻ
ॎԣʹ۠ΒΕͨ෦ʹࣈ͕ฒͿ
͍ΖΜͳߦྻ B C D E F G ߦྻYߦྻ
ߦྻYߦྻ B C D E F G H I J ߦྻYߦྻ
ߦྻͷ͠ࢉ ͠ࢉɺ෦͝ͱͷͷ ʢಉ͡ܗͷߦྻʹରͯ͠ఆٛ͞ΕΔʣ
ߦྻͷఆഒ ఆʢεΧϥʔʣഒɺͦΕͧΕͷ෦ΛLഒɻ
º ී௨ͷ
ߦྻͱߦྻͷֻ͚ࢉ º
ʁ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
Yߦྻ Yߦྻ
ߦྻͱߦྻͷֻ͚ࢉ º
ߦྻͱߦྻͷֻ͚ࢉ º
ߦྻͱߦྻͷֻ͚ࢉ º
✗
ߦྻͱߦྻͷֻ͚ࢉ "Y#ߦྻ $Y%ߦྻ º #$ͷ࣌ʹͷΈఆٛ͞Εɺ݁Ռ "Y%ߦྻ ʹͳΔ Ұൠʹɺ
ϕΫτϧ Y Z Y
Z P
ߦྻͱϕΫτϧ º /YߦྻͱΈͳͯ͠ɺ /Y/
/Y ͷֻ͚ࢉ͕Մೳ
ߦྻͱϕΫτϧ ݁Ռ/YߦྻͱͳΓɺ ϕΫτϧ͕ߦྻʹΑͬͯมԽͨ͠ɺͱղऍͰ͖Δ
º
ߦྻͱϕΫτϧ º
ߦྻͱϕΫτϧ º
ߦྻͱϕΫτϧ º
ߦྻͱม ˣ º
ٯͷม
º
ٯߦྻͱ୯Ґߦྻ
" " ? &
ಛघͳม
ٯߦྻଘࡏ͠ͳ͍ º º
ಛघͳม ٯߦྻଘࡏ͠ͳ͍ ˣ º
͓͠ͳ͕͖ w ߦྻͷ֓೦ w ߦྻͷ͠ࢉɺఆഒɺֻ͚ࢉ w ߦྻͱϕΫτϧ w ݻ༗ͱݻ༗ϕΫτϧ w
ߦྻͷ/
ݻ༗ͱݻ༗ϕΫτϧ " # " #
L มʹରͯ͠ɺେ͖͚͕ͩ͞มΘΔΑ͏ͳ ϕΫτϧ͕͋Δʢ߹͕͋Δʣ LΛݻ༗ɺɹɹɹΛݻ༗ϕΫτϧͱݺͿ " #
ݻ༗ͱݻ༗ϕΫτϧ
ʢ࣮ࡍʹɺ͜͜Ͱհͨ͠ݻ༗ϕΫτϧͷఆഒ ݻ༗ϕΫτϧʹͳΔʣ
ݻ༗ϕΫτϧͷҙຯ Y Z T U
ͱɹɹɹɹઢܗಠཱͳͷͰ ͜ͷΑ͏ͳT Uඞͣଘࡏ͢Δ
ݻ༗ϕΫτϧͷҙຯ Y Z T U
T U Tº Uº
ݻ༗ϕΫτϧͷҙຯ Y Z
Tº Uº ͱͱͷϕΫτϧ͕͍࣋ͬͯͨݻ༗ϕΫτϧͷΛɺ ͦΕͧΕݻ༗ഒͨ͠มʹͳΔ
ݻ༗ϕΫτϧͷҙຯ Y Z T
U Y Z T U T U Λ୯Ґͱ͢Δ ੈքʹม͑Δ
ݻ༗ϕΫτϧͷҙຯ Y Z T
U Y Z T U ݻ༗ഒ͢Δ
ݻ༗ϕΫτϧͷҙຯ
Y Z T U Y Z Y Z Λ୯Ґͱ͢Δ ੈքʹ͢
ݻ༗ϕΫτϧͷҙຯ
ߦྻͷ/
ߦྻͷ/
ߦྻͷ/ /
/
B C ߦྻͷ/ / B?/
C?/ / ?/ ?/
ϑΟϘφονྻ ʜ
ϑΟϘφονྻ B B B O B
O B O B O ΛɺOͷࣜͰද͍ͨ͠
ϑΟϘφονྻ ߦྻΛ͔͚ΔͱO͕ͭ૿͑Δ B O B O
B O B O
ϑΟϘφονྻ B O B O
B O B O B O B O
ϑΟϘφονྻ B O B O
B B / / ͕͔ΕɺҰൠ߲͕ग़ͤΔ
ϑΟϘφονྻ / ݻ༗ͱݻ༗ϕΫτϧΛग़͢͜ͱͰ/Ͱ͖Δ Ћ Ќ
Ћ Ќ / Ћ Ќ ͨͩ͠ɺЋ Ќํఔࣜ Y?Y ͷղ
ϑΟϘφονྻ B O ܭࢉ͢ΔͱʹͳΔ