This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of fields from linguistics finance. Typically, vectors are used to describe things that have magnitude and direction, and are therefore particularly useful for engineers and scientists when working with phenomena such as velocity, acceleration, momentum, force, impulse, weight, electromagnetic fields, and more. Vectors also have important applications in computer science such as computer graphics, machine learning and quantum computing. Other videos in this series cover calculating the magnitude of a vector, vector addition, scalar multiplication and calculating the dot product, cross product and convex combination of two vectors. Chapters: 00:00 Vector Applications 00:58 Visualising Vectors 02:18 Vector Notation 04:51 Two Dimensional Vector Space 06:52 Orthogonal Vectors 07:34 Three Dimensional Vector Space 08:15 Vectors for data analysis