Test vector

In computer science and engineering, a system is in effect a function. More precisely it is Computable function. The general function can be $y=f(x)$ . However, normally one does not conceive a system is one dimensional at all. For example a login page would have two inputs, an username/email id / password field. In that case, the login system can be described as:-

$y=L(u,p)$ with $y=\{true,false\}$ and $u,p\in \{String\}$, with True designating login successful, and False designating login failure, respectively. Clearly then the function login $L$ has 2 inputs.

Making things more generic, we can suggest that the function $L$ takes input as 2-dimensional vector and outputs a one dimensional vector ( scalar ). This can be written in the following way:-

$Y=L(X)$

with $X=[x_{i}]\;;\;Y=[x_{j}]$

In general the dimension of $X$ and dimension of $Y$ would differ. Therefore:-

$||X||\neq ||Y||$

Under this circumstances, the generalized system can be stated as:-

$Y=C(X)$ with $C$ belongs to computable functions.$X$ is called the input vector, and $Y$ is called the output vector.

Clearly then, to test the system we need to pass some sample vector $X_{i}$. In this context the $X_{i}$ is called a test vector.