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Scalar

Scalar Math is studied in linear Algebra where real number is considered as scalar and we can also relate the term scalar math with the vectors in vector space by using the operation known as Scalar Multiplication. In this operation a scalar or a number is multiplied by a vector to get back another vector.

We generally define a vector space with use of some field instead of using real number or scalar, and such field is known as Complex Number plane or field. The vector space or the Complex Plane has many scalar on its plane and these scalars are the elements of the field.

In scalar math, we have a matrix called scalar matrix which is used to denote a matrix in the form KI where k denotes a scalar and I is the identity matrix.

There is a big difference between scalar product operation and scalar multiplication operation. Scalar product is nothing but defined as the multiplication of two vectors to produce a scalar.
One more Point to be discussed in scalar math is that the vector space with the scalar product is known as an inner product space.

We should know that the real part component of a quaternion is also known as its scalar part.
The term scalar we use is sometimes used also in context with a vector or matrix or a compound when reduced to a single component. For instance, when we calculate the matrix product like 1 x n matrix and an n x 1 matrix, then it is generally called as a 1 x 1 matrix and it is usually known as a scalar.

Topics Covered in Scalar

Define Scalar

Scalar definition is not a new term for all of us; we have seen it when we talk about vectors. Definition of Scalar is studied in linear Algebra. We can define scalar by using the operation called Scalar Multiplication, where vectors in vector space are being multiplied by a real number so as to get another vector.
As you have seen above that how we have given the definit...Read More

Scalar Multiplication

Scalar multiplication is study under Scalar Math, where the word scalar is what which scales vectors. Scalar multiplication definition is different from scalar product definition which is nothing but an inner product between two vectors.
Scalar multiple is studied under the topic linear Algebra and if we talk about the simple definition, then it can be defined as ...Read More

Scalar Function

Function in general, is defined as any action or event performed by any person for which it is suited. In mathematical term, a function is defined as the relation of any variable with the other such that for each value of one variable, there exists a value for which second variable is also defined. It can also be defined as a Set, for which there exists a unique val...Read More

Scalar Field

In mathematics, scalar field is termed as a function, which gives us a single value of some variable for each and every Point in space. Scalar term can be composed of a mathematical term or a physical quantity. Scalar field should always be independent of coordinates which means that any two persons watching the objects will agree on same points of Scalar field in space. Te...Read More

Gradient of a Scalar Function

Slope or gradient refers to variation in space of a quantity. Gradient of any quantity reflects the steepness and direction of a line. The gradient of a Scalar function or field is a vector quantity that shows the direction of maximum rate of increase of that Scalar Field and magnitude will be equals to rate of increase.
Assume that there is a Scalar Funct...Read More

Scalar Potential Function

Function can be defined as a relation between inputs and outputs. A function normally relates each input exactly with one output.
Let’s take an example to define function properly in which 'x' is used as input and 'y' is used as output and suppose that relation between input 'x' and output 'y' is defined by rule 'y' = f(x).
Above rule says that output 'y' is ...Read More

Further Read

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