Vector Generalization

Learn the generality of vectors and the concept of operator overloading.

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We’ve described vectors as arrays of numbers having two key operations of addition and scalar multiplication. However, in linear algebra, a vector may be generalized as an object that fulfills the linear function properties of additivity and homogeneity. Therefore, besides number arrays, matrices, and polynomials, many other objects can also be taken as vectors if the operations of addition and scalar multiplication are defined for them.

Moreover, daily life objects, even with nonnumerical properties, can also be considered vectors. For example, humans can be modeled as vectors that have the properties of hobby, age, and name. The addition of these properties can be defined as the concatenation of the names and the addition of the ages.

Note: Like vectors, scalars also aren’t limited to real or complex numbers.

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