Applications of Basis and Dimension of Vector Space.

Quantum Mechanics:

Quantum Mechanics is entirely base on it. Also important for time domain (state space) control theory and stresses in materials using tensors.

Most commonly in physics, vectors are used to represent displacement, velocity, and acceleration. Vectors are a combination of magnitude and direction, and are drawn as arrows. The length represents the magnitude and the direction of that quantity is the direction in which the vector is pointing.

Designing bridges:

The natural frequency of the bridge is the eigenvalue of smallest magnitude of a system that models the bridge. The engineers exploit this knowledge to ensure the stability of their constructions.

Linear operator plays a key role in computer graphics. For many CAD software generates drawing using linear operators, and do not forget about cryptography.

Dimension: the length, width, height, or depth of something: a measurement in one direction (such as the distance from the ceiling to the floor in a room): the amount or number of things that something affects or influences. : A part of something.


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