I never heard this at school, then I realised that you were talking about computers, photoshop, etc. These never existed when I was in school, the slide rule was the most advanced device used in maths. Great time to be alive and l really like your explanations. A 72 year old!
I love you more every time I hear you say “show your work.” Also, when you say things like “divide both sides by 7” or “add 7 to both sides.” Sometimes teachers leave the last two things out and turn them into something magical by saying, “move the -2 to the other side of the equation and make it positive,” 😬 when what they should have said, is “add 2 to each side of the equation.” I never did become a teacher, as I would have liked, but I did a lot of tutoring. This gave me the opportunity of seeing what different instructors were saying to people and goofing them up. I got to where every time I heard a student say the word “move” I would be like “No, you’re not moving anything! What are you doing to both sides of the equation to keep it equal?” I won’t even get started on the silly things instructors do to my favorite subject, trigonometry, in order to thoroughly confuse the students. “Whenever possible, understand, don’t memorize,” is my motto. Anyway, I really appreciate that you never make magical things happen on your drawing board. 😉👍🏻
The determinant does have intrinsic meaning. It's the opposite of the dot product, it's a test of the orthogonality of the basis. So, the identity, which is orthonormal, returns 1. Perfect orthogonality. Mat(vec(1, 0), vec(1, 0)) returns zero. They have a dot of 1 and a determinant of zero. Mat(vec(-1, 0), vec(1, 0)) is also zero. Parallel. Mat(vec(1, 0), vec(0, -1)) perfectly orthogonal. -1. So with normalized vectors it's essentially the inverse of the dot. The sine to the cosine. It's only when the magnitude is not normalised that you get large numbers, same as the dot.
Since learning statistics, I find myself thinking that determinants are analogous to the measures of central tendency (mean, mode, range) in that they both describe a set of data - and they both do it inadequately.
Say you go to the gym and lift weights. You improve your muscle strength, makes your body work better. Math does for your brain what weights do for your body. It teaches you how to understand complex ideas and structures, makes you be better at solving all sorts of non-math problems.
Matrices are just a good way to organize data. They're used in many fields. The simplest case is that its used to model motion of an object in some space for example
It helps to manipulate an object from one dimension to another. If you have used Photoshop to flip, rotate, resize, or bend your image, then matrices and determinants were used.
I never heard this at school, then I realised that you were talking about computers, photoshop, etc. These never existed when I was in school, the slide rule was the most advanced device used in maths. Great time to be alive and l really like your explanations. A 72 year old!
I love that you fully explain everything.
I love you more every time I hear you say “show your work.” Also, when you say things like “divide both sides by 7” or “add 7 to both sides.” Sometimes teachers leave the last two things out and turn them into something magical by saying, “move the -2 to the other side of the equation and make it positive,” 😬 when what they should have said, is “add 2 to each side of the equation.” I never did become a teacher, as I would have liked, but I did a lot of tutoring. This gave me the opportunity of seeing what different instructors were saying to people and goofing them up. I got to where every time I heard a student say the word “move” I would be like “No, you’re not moving anything! What are you doing to both sides of the equation to keep it equal?” I won’t even get started on the silly things instructors do to my favorite subject, trigonometry, in order to thoroughly confuse the students. “Whenever possible, understand, don’t memorize,” is my motto. Anyway, I really appreciate that you never make magical things happen on your drawing board. 😉👍🏻
The determinant does have intrinsic meaning. It's the opposite of the dot product, it's a test of the orthogonality of the basis. So, the identity, which is orthonormal, returns 1. Perfect orthogonality. Mat(vec(1, 0), vec(1, 0)) returns zero. They have a dot of 1 and a determinant of zero.
Mat(vec(-1, 0), vec(1, 0)) is also zero. Parallel.
Mat(vec(1, 0), vec(0, -1)) perfectly orthogonal. -1.
So with normalized vectors it's essentially the inverse of the dot. The sine to the cosine.
It's only when the magnitude is not normalised that you get large numbers, same as the dot.
I’m watching this video since it was recommended in my feed and I’m bored. Loved your explanation on the video!!
Since learning statistics, I find myself thinking that determinants are analogous to the measures of central tendency (mean, mode, range) in that they both describe a set of data - and they both do it inadequately.
I love that colleges make us take math and work is hard for 3 months, then we never see or use this stuff again....
Depends on your career.
I love that I do weightlifting and I never ever have to lift up dumbbells anywhere else.
I use it in the store, my work, when trying to figure out women...
Say you go to the gym and lift weights. You improve your muscle strength, makes your body work better. Math does for your brain what weights do for your body. It teaches you how to understand complex ideas and structures, makes you be better at solving all sorts of non-math problems.
So true
Determinants: they are scalar quantities obtained by the sum of products of the elements of a square matrix and their cofactors .
Wow!
Hello, Thank you for sharing how to treat a matrix. But, what is a matrix good for?
Matrices are just a good way to organize data. They're used in many fields. The simplest case is that its used to model motion of an object in some space for example
It's part of how Photoshop exists.
What is the point? A purpose was never stated.
Greetings. The answer is 26. Determined as follows (4×8) -(3×2) = 32-6=26. What is it called again, determinant?
Determinant, product of a matric, answer is 26
Why would you arrange these numbers in a matrix. What kind of a problem is it meant to solve.
It helps to manipulate an object from one dimension to another.
If you have used Photoshop to flip, rotate, resize, or bend your image, then matrices and determinants were used.
What a matrix!!!
Shows what I know, I didn't even know this was a math problem.
A 2x2 matrix is so easy to solve. Let's try solving a 5x5 matrix.
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Ps. "Matrix" understood as a couple of rows and columns of numbers.
All i see is a matrix. Until you tell me for what you are trying to solve, it is just a matrix.
+4+2
+3+8
=======
32--6===26
Exactly. WHAT is this!? Guess I will find out.
26
notes: a+b-c = sandwich
Almost 4 min to get to any content. Stop the Opening Ramble! Great content once you get going.
For me it was about 5 1/2 mins.
Agreed, to much talking...
Determinants
SOOOO long winded!!
9 minutes in and I'm getting bored
You talk to much instead of getting to the point of solving the problem no disrespect broi mean none at all
Fasse dich kurz!
26