Query regarding Mathematics Final Exam
Final Exam Q17: You have not explained the concept of orthogonal vectors in the course. What are they and what are their properties?
thanks for reaching out!
Orthogonal vectors are vector which are perpendicular to each other and their dot product is 0. An example would be
vectors [1, 0]Т and [0,1]T, as they're dot product is 1*0 + 0*1 = 0
Let me know if you have any further questions on the topic.
Hi, Thanks for the brief explanation. Can you please also elaborate a few important noteworthy characteristics of orthogonal vectors? As a short term action, may I suggest to include some description or a lesson regarding orthogonal vectors in the Mathematics course? Or please send me a link in case some info is available within some other courses.
thanks for the suggestions, we'll add a short lecture on orthogonal vectors or revise the course exam to include only relevant materials. In terms of further reading this lecture is short and precise:
As an addition to that the importance of orthogonal and orthonormal vectors comes in using orthogonal functions, basis or spaces. For example, you can use orthogonality and trigonometric functions to approximate given functions. Most of these concepts go beyond what we cover in the program, as they require a more rigorous mathematical training. We do touch upon linear span and basis in this course:
And though not explicitly specified in the course, the PCA transformation is an orthogonal projection on to a lower dimensional space.
Hope this helps!