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Daha fazlası ve ders videolarını sıralı izlemek için: https://www.khanacademy.org.tr Matematikten sanat tarihine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/751132/7ecf75fcce90d29f687064862eda38cb/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/foF1OgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1769845835880732-14107208061613436812-balancer-l7leveler-kubr-yp-vla-64-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769845835880732-14107208061613436812-balancer-l7leveler-kubr-yp-vla-64-BAL&text=videoid:6569053102659684394","teaser":[{"list":{"type":"unordered","items":["Bu video, bir eğitmen tarafından sunulan matematik dersi formatındadır.","Videoda, sıfırdan farklı iki vektörün (x ve y) nokta çarpımlarının mutlak değerinin, uzunluklarının çarpımından küçük veya eşit olduğu Cauchy-Schwarz eşitsizliği ispatlanmaktadır. Eğitmen, eşitsizliğin koşullarını açıklamakta, bir fonksiyon tanımlayarak ispat sürecini adım adım göstermekte ve vektörlerin büyüklükleri, nokta çarpımları ve skaler çarpımlar gibi kavramları kullanmaktadır.","Videoda ayrıca, bir vektörün diğerinin skaler bir katı olduğunda eşitsizliğin eşitlik durumunda olduğu açıklanmakta ve Cauchy-Schwarz eşitsizliğinin nokta çarpıma göre neden daha mantıklı olduğu konusunda gelecek bir videoda detaylıca ele alınacağı belirtilmektedir."]},"endTime":937,"title":"Cauchy-Schwarz Eşitsizliği İspatı","beginTime":0}],"fullResult":[{"index":0,"title":"Vektörlerin Nokta Çarpımı ve Koşulları","list":{"type":"unordered","items":["Sıfırdan farklı iki vektör x ve y, R üzeri n kümesinde yer alıyor.","İki vektörün nokta çarpımlarının mutlak değeri, uzunluklarının çarpımından küçük ya da eşittir.","Nokta çarpımlarının mutlak değerinin uzunlukların çarpımına eşit olduğu tek durum, vektörlerden birinin diğerinin skaler bir katı (eş-dörusal) 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