Linear algebra 2 - Lengths and dot products скачать в хорошем качестве

Linear algebra 2 - Lengths and dot products

In this video, we will explore the relationship between lengths and dot products. By first defining the dot (inner) product, we can derive some very fascinating properties, and eventually we realize a beautifully woven relationship between the dot product of two vectors with their lengths. More precisely, the dot product is also a measure of the cosine of the angle between the two vectors, scaled by the product of the two vectors' lengths. The dot product is a fundamental operation in linear algebra and multivariable calculus, which we will see next in our journey of linear algebra. Video and editing: William Tu End music: Nikolai Kapustin - Piano Sonata No. 2, Op. 54 bmp6IG5ldmVyIGRpZXM=