Non-zero orthogonal vectors are vectors that are perpendicular to each other, meaning that they form a 90 degree angle between them. This means that their dot product is equal to 0.
In this context, m<=n means that the number of non-zero orthogonal vectors (m) is less than or equal to the dimension of the vector space (n).
This can be shown through a mathematical proof, where m and n are represented as variables and the properties of non-zero orthogonal vectors are used to demonstrate that m<=n is true.
Some examples of non-zero orthogonal vectors include (1,0) and (0,1) in a 2-dimensional space, or (1,0,0) and (0,1,0) in a 3-dimensional space. These vectors are perpendicular to each other and have a dot product of 0.
Non-zero orthogonal vectors are important in science because they allow us to represent and manipulate data in multiple dimensions. They are also used in fields such as physics, engineering, and computer science to represent forces, velocities, and other important quantities.