VECTOR SUBSPACES
In the article An Introduction to Vector Spaces, the meaning of vector and vector space are presented . Since a vector space is a set (with a bundle of properties), a question that can be raised is: “Are subsets ofRead More
AN INTRODUCTION TO VECTOR SPACES
The term vector is much found when we study physics or mathematics. What is the meaning of a vector, actually? In this post, the general definition of vectors will be discussed. Below is the definition of a vector space. Read More
THE CENTROIDS OF SPECIAL-TYPED TRIANGLES
While the article The Centroid of A Triangle explains how to find the centroid of any triangle, this article elaborates on how to determine the centroids of some special-typed triangles, that is isosceles, equilateral, and right-angled triangles. The CentroidRead More
COVARIANCE AND CORRELATION MATRICES
Variance and correlation matrices play a vital role in multivariate statistics. Multivariate statistics studies n x p data from a set of samples, where n is the sample size or the number of measurements and p is the number ofRead More
CONTINUITY OF A FUNCTION AT A POINT
Consider the real-valued function f defined by for every real number. Note that the function returns the greatest integer less than or equal to x. The graph of f is portrayed below. As can be seen from the graph, thereRead More
THE LIMIT OF A FUNCTION AT A POINT
Let f be a real-valued function with f(x) = x + 5 for every real number x. Let’s consider the values of f(x) when the values of x are around 2, but x ≠ 2. ( See Table 1 below.)Read More
POINT OF INTERSECTION OF TWO LINES
If two coplanar lines are not parallel then they intersect each other. Furthermore, if they are placed on the Cartesian plane, we can determine the coordinates of the point of intersection. Suppose we are given the line g and hRead More
THE SPECTRAL DECOMPOSITION OF SYMMETRIC MATRICES
The picture above is an application of singular value decomposition in image processing. This post will discuss a special case of SVD, where the matrix to be decomposed is a symmetric matrix. The study of symmetric matrices is important inRead More
THE CENTROID OF A TRIANGLE
Suppose that ∆ABC is any triangle. To determine its centroid, draw the median passing through one of its vertices, A. Let D be the midpoint of the line segment BC. (So the median passes through A and D.) Similarly, drawRead More
INDEPENDENT EVENTS
The above symbols represent the 52 cards of a deck of playing cards. If a card is selected at random from the deck then each of the 52 signs above is a member of the sample space. So the sample spaceRead More