Vector Algebra

It is possible to have multiple names for the set of scalars associated with a linear system of equations (in this case, a matrix equation), such as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144) or latent roots (Hoffman and Kunze 1971).  This is […]

Eigenvalues are a unique collection of scalar values linked to a set of linear equations, most commonly in matrix equations. Eigenvalues are also called characteristic roots or latent roots. After applying linear transformations, it is a non-zero vector that its scalar factor can only alter. An eigenvalue is the scale factor that correlates to the

A zero vector, also known as a null vector, has a magnitude of 0 and no direction. To understand the zero vector in further depth, let us first review what a vector is and what it means to be zero. Generally speaking, a vector is a geometric item or object with both a magnitude (length)

Vedic Mathematics are the set of sutras for solving mathematical problems rapidly and efficiently. These cheats demonstrate how to apply arithmetic computation, number theory, mathematical and algebraic operations, higher-level mathematics, calculus, and coordinate geometry, among other topics. It is essential to teach children some Vedic mathematical skills and concepts at a young age in order

Vectors and scalars are used in calculations to represent physical quantities mathematically. Each physical quantity may be classified as a scalar or a vector quantity. When data are expressed in scalar or vector form, the computation is far easier. Discover how to distinguish between vector and scalar values, the mathematical procedures that apply to them,

Vector arrows depicting magnitude are the foundation of logical statements in mathematics. There are certain types of vectors; however, all vectors are categorised into two types: unit vector and zero Vector. Any form of vector with no magnitude and coordinates is categorised as zero vectors, and the remaining ones are unit vectors.  Vectors have associative

What is a vector? Geometrical elements with direction and magnitude are known as vectors. A vector is represented as a line with an arrow pointing in the direction of the vector, and the length of the line denotes the vector’s magnitude. As a result, arrows represent vectors and have two points: an initial point and

A vector space, also known as a linear space, is a collection of items known as vectors that are put together and multiplied (“scaled”) by numbers known as scalars. Scalars are commonly thought of being real numbers. With vector spaces, however, there are only a few cases of scalar multiplication by rational numbers, complex numbers,

Equality of Vectors Two vectors a and b are said to be equally written as a = b if they have (i) the same length, (ii) the same or parallel direction/support, and (iii) the same sense. Types of Vectors Zero or Null Vector: A vector whose initial and terminal points are coincident is called a

Vectors are useful in our everyday lives. However, in the real world, events take place in three dimensions. In general, we learn to solve vectors in two dimensions. However, to enhance the usage of vectors in more realistic applications, it is necessary to explain vectors in terms of three-dimensional planes. Let us first start with