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The most useful stl container is vector. A stl::vector is a sequence of elements of a given type. The elements are stored contiguously in memory. So a STL vector is a collection of values of the same type—in this way it's like the mathematical meaning of vector/module—but the main issue is how elements are stored.
So the abstracted properties appear in the definition of a vector space, not in the definition of a vector. The original geometric content of a vector appears only later as a very special case, when a real vector space acts on a (real) affine space as its space of translations, and when these translations are depicted eg. by arrows.
The first definition is of an external direct sum, whereas the second definition is of an internal direct sum. See here , for example. These definitions are isomorphic.
To normally compute the length of a vector, you might use a dot product with itself and take the square root, but I'll show here that the dot product is vulnerable to changes in coordinate systems. That will be why I bring in covectors to solve this problem - though the difference is very subtle. Definition of vector
The definition of a Vector space allows us to add two vectors, subtract two vectors, and multiply a vector by a scalar. When it comes to multiplying two vectors you have the dot product and the cross product. However, the dot product gives a scalar as output. This leaves us with the cross product whose result is a vector.
That is the correct definition in physics. If you incorporate the correct definition of a vector in maths, you can easily understand the "direction" concept alternatively. In physics the direction associated with a vector means you first fix a coordinate system and see in which direction the effect of the vector is as a whole.
If that's the case then a vector acts on a scalar field and tells me how the field changes on that point. However, if a vector is a derivative operator, a vector field defines a different derivative operator at each point. So differentiate a vector would be differentiate a derivate operator, and that seems strange to me at first.
The tutorial simplifies and that can cause confusion. Its definition describes "basic vector types", but there are also "generic vectors". From the language definition (which you should study): 2.1.1 Vectors. Vectors can be thought of as contiguous cells containing data. Cells are accessed through indexing operations such as x[5].
//The static keyword is only used with the declaration of a static member, //inside the class definition, not with the definition of that static member: std::vector<int> Foo::MyVector = {4, 17, 20}; Share
A vector is similar to an Array. A vector holds multiple number values. In Python, you can do operations on vectors using things like dot product and cross product, in linear algebra. These operations are used to efficiently manipulate data when creating neural networks and 3d rendering.