Define Scalar Define Scalar In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations (in Newtonian mechanics), or by Lorentz transformations or space-time translations (in relativity). A scalar is a quantity which can be described by a single number, unlike vectors, tensors, etc. which are described by several numbers which describe magnitude and direction. A related concept is a pseudoscalar, which is invariant under proper rotations but (like a pseudovector) flips sign under improper rotations. The concept of a scalar in physics is essentially the same as in mathematics. An example of a scalar quantity is temperature; the temperature at a given point is a single number. Velocity, for example, is a vector quantity. Velocity in three-dimensional space is specified by three values; in a Cartesian coordinate system the values are the speeds relative to each coordinate axis.
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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 definition of scalar, actually, the Real Numbers used to multiply with the vectors are known as scalars. The term vector space used while defining the scalar is nothing but the field which uses complex numbers instead of using real numbers in the field. Then we will say that scalar definition or scalars of that particular vector space or field will be the elements of the space or field. The definition of scalar includes two types of operation in it: scalar product and scalar multiplication, we should not get confused between them. We can also define scalar by the operation scalar product where we produce a scalar, when the two vectors in vector space are allowed to multiply with each other. When we have a scalar product in our vector space or field, then that vector space is known as an inner product space. We can give the scalar definition by using a quaternion also, where the real component or real part of it is known as its scalar part or component. We have a matrix in scalar Math called scalar matrix by which we can denote a matrix of the form KI, where K is nothing but a scalar and I is an identity matrix. We can also define scalar by using words like vector, matrix, etc. So we can generalize it by the product of a 1xn matrix and an n x 1 matrix, which is a 1x1 matrix and is normally known as a scalar.
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Real function: A function is said to be a real function if its range lies between Real Numbers that is negative infinite value to positive infinite value. Complex function: A complex function is defined as a function which contains real as well as imaginary numbers in its domain and range. Scalar function: Any function which contains one or more variable and its range is one dimensional is known as scalar function. Vector function: A function is said to be a vector function if it contains one or more variables and its range is three dimensional.
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