William Rowan Hamilton, the Irish Genius.
A scalar is a magnitude only (...I am driving at 60 miles per hour), while a vector is a magnitude and direction (...I am driving at 60 miles per hour, heading east).
Scalars are not always negative. The word scalar means that a value behaves like the numbers we are familiar with. You just add and subtract them. These are different than vectors, where you need to break them into scalars in order to add them first.
Basis vectors are fundamental vectors in a vector space that define its structure and orientation. In the context of a transformation, they serve as the building blocks from which other vectors can be expressed as linear combinations. When a transformation is applied, the basis vectors are mapped to new vectors, allowing for the representation of the entire vector space in a transformed coordinate system. This concept is crucial in fields like linear algebra and computer graphics, where transformations are frequently utilized.
Linearly independent vectors are a set of vectors in which no vector can be expressed as a linear combination of the others. This means that the only solution to the equation formed by setting a linear combination of these vectors to zero is that all coefficients must be zero. In other words, if you have a collection of linearly independent vectors, removing any one of them would alter the span of the set. This concept is fundamental in linear algebra, particularly in determining the dimensionality of vector spaces.
pestaloggi
Austin
Georges Lemaitre gave the concept of Explosion. Sir Edwin Hubble gave the concept of Expansion.
In solid-state physics, "basis" refers to a set of vectors that define a crystal's lattice structure and play a fundamental role in describing the periodicity of the crystal. By combining the basis vectors with translation vectors, we can reproduce the entire crystal lattice. This concept is crucial for understanding the electronic and vibrational properties of solids.
No, vectors are not just a convenience in expressing physical quantities. They have magnitude and direction, which makes them essential in describing physical quantities like force, velocity, and acceleration accurately in three-dimensional space. Vectors are fundamental in physics and mathematics for representing quantities that have both magnitude and direction.
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M K Gandhi
Georg Cantor