If u and v are two vectors, then as per the Cauchy-Schwarz inequality, the magnitude of the dot product between these two vectors is no longer than the product of the norms of these two vectors. In other words, $latex |\vec{u} \cdot \vec{v}|\leq ||\vec{u}||||\vec{v}||...

What is a vector dot product and how to calculate it? Let’s say a and b are two n-dimensional vectors. If we perform a dot product or scalar product of a and b, the corresponding elements of the two vectors get multiplied and then, the resultant terms are added to get...

How to perform vector and scalar multiplication? If we multiply a vector with a scalar, then each component of the vector gets multiplied by the scalar. For example, let’s say r1 is a row vector, c1 is a column vector and λ is a scalar. At this point we can multiply λ...

How to perform vector addition and subtraction? Let’s say v1 and v2 are two row vectors with the same dimension. If we add the two vectors v1 and v2, then we will get another vector v3 that will have the same dimension as v1 and v2. And each component of v3 will be...

What is the transpose of a vector? We know that a row vector can be represented using a 1xn matrix. And a column vector can be represented using an nx1 matrix. Let’s say v1 is a row vector and v2 is a column vector. And v1 and v2 have the following components: $latex...