I'm not sure, what a "real time" means in your question. Usually this term means, that the data processing does not require more time than the data acquisition, such that both can be done simultaneously.
In the real world we are familiar with scalars everywhere, e.g. the current temperature or the price of a banana.
Now imagine, that you want to store a bunch of values, e.g. the temperature for every minute of a day. This can be stored in a list intuitively, and this list is called a "vector". Now you can compare two temprature vectors, e.g. one recoreded in the winter, one in the summer. You see different absolute values, but similar shapes (its warmer during the sun shines).
Such vectors can be interpreted as coordinates in a space. A standard example is the position in the 3D space: r = [1, 2, 3] can mean a point, which is 1m to front, 2m to the left and 3m on top of the local origin (e.g. your eye or right foot). A 4D vector can be r = [1,2,3,36.5], ehich can be the 3D position and the temperature as 4th component.
If you now want to do some operations with the vectors, you need matrices: e.g. the rotation of a point around the origin can be expressed by a rotation matrix of size [3x3]. Such rotation matrices have interesting properties, but this is another story. Beside the function as an operator, a matrix can be seen as "vector of vectors" also, e.g. a [3 x 1] list of [1 x 3] vectors.
The cross-product has a geometrical meaning: The cross(a,b) with a and b are 3D vectors, is a vector, which is perpendicular to a and b, while the length is determined by the included angle.
Welcome to the world of applied mathematics. Usually the contributors in this forum have a certain level of mathematical knowledge already. Therefore this forum is not the right location to learn the basic of linear algebra - as long as there is no relation to the programming language MATLAB.
T. Hund said: "Numbers are an attack to the independence." A positive interpretation is, that numbers and computations with them are used to control conflicts of interests or opinions. E.g. the question "is Kofi Annan tall" can be discussed and decided much easier, when we use numbers to parameterize the term "tall". A negative interpretation is, that numbers let mathematicians look sophisticated and let bankers get rich. In the Stone Age human worked two hours a day for food and accommodation. Therefore it's questionable, if numbers are an advantage at all.
