2:35 i cant understand why costheta is cant be greater than 0. isnt it all about the angle of between two vectors? why the angle is cant be smaller than 90 degrees.
Thanks a lot sir.... u did a commendable job by makin these..... Ur videos helped me alot alot ..... I without any doubt herald that there's no maths teacher in my institution who teaches concepts like you teach....
Thank you very much. You uploaded this in 2012 and it helped me in 2020 :) which is an indication that whatever good we do, let's just do it. We don't know at what time in life that good things will benefit people. Maybe the effect will appear long after we die. So let's not always try to see an immediate effect of the good we do in our life : )
shouldn't the second order condition be that the double derivative of the function is less than zero for a (strict) maximum and greater than zero for a (strict) minimum ? I think you got the signs wrong there.
Hi. First of all, I just want to say thank you so much for this playlist. Secondly, I have a question. In this video, you show that if the upper left determinants of A are both positive for a (2,2) matrix, then the matrix is positive definite, and the equation X^T AX = f(X) (where X is some vector) will have a minimum at x=0. You did so by completing the square. However, how would we show that the upper determinant test also checks for positive definiteness for bigger matrices? I tried completing the square for X^T AX in the case that A was (3,3), and that was WAAAY too ugly. There's gotta be a better way! Thanks!
I am confused on the augmented matrix for the example. Where did the first linear equation arrive with a 2 to start? Shouldn’t it have been (0,0,1) as the initial augmented matrix
EUCLIDEAN SPACE References Geometry | Definition of Geometry by Merriam-Websterwww.merriam-webster.com/dictionary/geometry Definition of geometry for Students. : a branch of mathematics that deals with points, lines, angles, surfaces, and solids. Two-dimensional definition and meaning | Collins English Dictionarywww.collinsdictionary.com/dictionary/english/two-dimensional two-dimensional. A two-dimensional object or figure is flat rather than solid so that only its length and width can be measured. Three-dimensional definition and meaning | Collins English Dictionarywww.collinsdictionary.com/dictionary/english/three-dimensional A three-dimensional object is solid rather than flat, because it can be measured in three different directions, usually the height, length, and width. ... Rhetorical Questions 1. Are electromagnetic particles flat, or are they infinitesimal quanta’s of radiant energy that exist in the form of infinitesimal spheres of spinning and radiating particles of electromagnetic influence? 2. Are atoms flat or are they composites of infinitesimal quanta's of radiant energy orbiting around the central gravitational nucleus of an atom, within the limits of its gravitational field and its surrounding space? 3. Can anything of the physically apparent (macro-cosmic) cosmos be straight or flat, as all physical things of the macro-cosmic universe are constructed from composites of infinitesimal (microcosmic-quantum) electromagnetic (gravitational) particles, which spin and (centrifugally) radiate their spheres of electromagnetic influence outward into all sectors of their immediate surrounding space? 4. Given, that the space surrounding each of us, and our planet, are extents of voluminous emptiness. How in logic and in rationality can it be claimed, that the mathematical propositions of Euclid’s straight linear geometry, can be applied, to what is essentially directionless non-geometrical empty space? Euclidean Linear Definitions Euclid A line is a breadth-less length. Reality Only within the imagery of the mind’s eye e.g. the imaginary lines between the stars of the constellations, whereas the lines of linear drawn geometry possess both a length and a width of surface area to their presence. Euclid A point is that which has no part. Reality Only within the imagery of the mind’s eye. A point in linear drawn geometry, possesses an amount of surface area with a graphite particle or coloured pigment coverage. Euclid A straight line is a line which lies evenly on itself. Reality A straight line is a line which lies evenly *of* itself over an evenly straight flat surface. Euclid A surface is that which has length and breadth only. Reality A surface is that which has length breadth and depth. Euclid The Extremities of a surface are line. Reality The extremities of a surface relative its shape, is its naked edge. The extremities of surface to a solid, is governed by its volume. The volumes of ovoid’s and spheres do not have any extremities to the curvature of their surface. www.fromthecircletothesphere.net
I take this course as theoretical math., so finding static optimization videos teaching the way you do helps quite a lot!! Thank you for your work, I just wanted to say that I appreciate it. The lessons are easy to follow and clear!
