Yes and no. In the finite dimensional case a vectorspace and its dual are isomorphic, so every vector - basis or not - can as well be seen as a dual vector. It might become clearer if you regard a vector as a column vector and its dual vector as the same written in a row.nabeel17 said:So are basis vectors actually dual vectors?
A vector transformation law is a mathematical rule that describes how a vector (a quantity with both magnitude and direction) changes when it is transformed from one coordinate system to another.
The vector transformation law involves complex mathematical concepts such as linear algebra and matrix operations, which can be challenging to understand for those without a strong mathematical background. Additionally, grasping the concept of transforming vectors from one coordinate system to another can be difficult for some individuals.
The vector transformation law is used in various scientific fields, such as physics, engineering, and computer science, to describe the movement and behavior of objects and systems in different coordinate systems. It is particularly useful in understanding and solving problems involving motion, forces, and transformations of coordinates.
Some common examples of vector transformation include converting between different units of measurement (e.g. converting velocity from meters per second to miles per hour), rotating a vector in two or three-dimensional space, and transforming coordinates from a Cartesian system to a polar system.
To better understand the vector transformation law, it is helpful to have a strong foundation in linear algebra and matrix operations. Practice with solving problems and visualizing vector transformations can also improve understanding. Additionally, seeking guidance from a tutor or professor can be beneficial in clarifying any confusing concepts.