Mathlab for students

Bouncing ball in box

uses the y=mx+c property

k-means clustering is a partitioning method. The function kmeans partitions data into k mutually exclusive clusters, and returns the index of the cluster to which it has assigned each observation. Unlike hierarchical clustering, k-means clustering operates on actual observations (rather than the larger set of dissimilarity measures), and creates a single level of clusters. The distinctions mean that k-means clustering is often more suitable than hierarchical clustering for large amounts of data.

kmeans treats each observation in your data as an object having a location in space. It finds a partition in which objects within each cluster are as close to each other as possible, and as far from objects in other clusters as possible. You can choose from five different distance measures, depending on the kind of data you are clustering.

Each cluster in the partition is defined by its member objects and by its centroid, or center. The centroid for each cluster is the point to which the sum of distances from all objects in that cluster is minimized. kmeans computes cluster centroids differently for each distance measure, to minimize the sum with respect to the measure that you specify.

Fit probability distributions to sample data, evaluate probability functions such as pdf and cdf, calculate summary statistics such as mean and median, visualize sample data, generate random numbers, and more. Work with probability distributions using probability distribution objects, command line functions, or interactive apps. For more information about each of these options.

Quaternions are vectors used for computing rotations in mechanics, aerospace, computer graphics, vision processing, and other applications. They consist of four elements: three that extend the commonly known imaginary number and one that defines the magnitude of rotation. Quaternions are commonly denoted as:

q = w + x*i + y*j + z*k where i² = j² = k² = i*j*k = -1

This rotation format requires less computation than a rotation matrix.

Common tasks for using quaternion include:

Converting between quaternions, rotation matrices, and direction cosine matrices

Performing quaternion math such as norm inverse and rotation