The cross product is an operation exclusive to three-dimensional vectors that results in a vector perpendicular to both of the vectors being multiplied. Let’s begin…

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In linear algebra, the outer product of two vectors produces a matrix. Each element in this matrix is the product of elements from the two…

Hadamard multiplication, also known as element-wise multiplication, involves multiplying two vectors of the same dimension, element by element. Let’s begin by examining two column vectors:…

The angle between two vectors represents the spatial relationship or orientation between them. A smaller angle means the vectors are more closely aligned, while a…

The magnitude or length of a vector is a measure of its size. This metric is commonly referred to as the Euclidean norm of a…

The dot product multiplies corresponding components of two vectors and sums the results. One critical condition for calculating the dot product is that both vectors…

A scalar is simply a single number. It can be thought of as a vector with a single dimension, representing only magnitude without direction. Scalar…

Adding and subtracting vectors are essential operations that allow us to manipulate vectors for various applications, from physics to computer graphics. These vector operations, central…

A 3D vector extends the concept of a 2D vector into three dimensions. It is an ordered set of numbers that comprises three elements often represented…

A vector is simply an ordered set of numbers. The dimension of a vector is determined by the number of elements it contains. In the…