Parth G | The Math Found EVERYWHERE in Physics: MATRICES - Get Ahead by Learning This Topic @ParthGChannel | Uploaded 3 years ago | Updated 3 hours ago
This is the math topic that you should learn if you'd like to understand advanced physics concepts more easily!
Matrices and matrix algebra in general is a very useful topic to understand, and the basics are actually quite simple! Many of you have asked me for my recommendation on one topic to learn in order to pick up advanced physics concepts more easily - and this is it!
I wanted to discuss how particular properties of matrices correspond directly to particular requirements of physics theories. This is, of course, in part because those theories were formalized using matrices in the first place... but not always.
For example, those of you familiar with matrix multiplication will know that this process is not commutative - the order in which you multiply two matrices together actually matters. If we want to multiply matrices A and B, then the product AB is not necessarily the same as BA. This is known as the non-commutativity of matrix multiplication.
This non-commutative property is perfect for representing measurement operators in quantum mechanics! When we make multiple measurements on a quantum system, the order in which we make these measurements actually matters. For example, measuring the position and then the momentum of an electron can give us different results to measuring the momentum first and then the position. Measurements in quantum mechanics are mathematically represented by "measurement operators" (discussed here: https://www.youtube.com/watch?v=so1szjHu7jY), and these can be easily represented by matrices!
In my previous video (before this one), we talked about Einstein's Field Equations of General Relativity (https://www.youtube.com/watch?v=FJnTItLVIqQ). We saw that the equations are a way to link the stress-energy tensor to the Einstein tensor representing the curvature of spacetime - in simple terms, how mass and energy warps spacetime. As it turns out, tensors are extremely interesting mathematical objects that can easily be represented by matrices! Linear algebra is a very useful topic to study for General Relativity.
Now I've mentioned the two coolest (in my opinion) examples above - but matrix algebra is useful in other areas of physics too. Fluid dynamics, classical mechanics, you name it, you'll likely find matrices there. So I'd recommend learning things like matrix multiplication, matrix inversion, solving simultaneous equations with matrices, and more. Anything to help you get a better grasp of the topic. Because if you come to advanced physics concepts with a solid mathematical grasp of matrices, then you'll be able to spend more time understanding the physical interpretations of the physics you are learning!
Thanks so much for watching this video! If you enjoyed it, please do like and subscribe. Check out my socials too!
Instagram - parthvlogs
Patreon - patreon.com/parthg
This is the math topic that you should learn if you'd like to understand advanced physics concepts more easily!
Matrices and matrix algebra in general is a very useful topic to understand, and the basics are actually quite simple! Many of you have asked me for my recommendation on one topic to learn in order to pick up advanced physics concepts more easily - and this is it!
I wanted to discuss how particular properties of matrices correspond directly to particular requirements of physics theories. This is, of course, in part because those theories were formalized using matrices in the first place... but not always.
For example, those of you familiar with matrix multiplication will know that this process is not commutative - the order in which you multiply two matrices together actually matters. If we want to multiply matrices A and B, then the product AB is not necessarily the same as BA. This is known as the non-commutativity of matrix multiplication.
This non-commutative property is perfect for representing measurement operators in quantum mechanics! When we make multiple measurements on a quantum system, the order in which we make these measurements actually matters. For example, measuring the position and then the momentum of an electron can give us different results to measuring the momentum first and then the position. Measurements in quantum mechanics are mathematically represented by "measurement operators" (discussed here: https://www.youtube.com/watch?v=so1szjHu7jY), and these can be easily represented by matrices!
In my previous video (before this one), we talked about Einstein's Field Equations of General Relativity (https://www.youtube.com/watch?v=FJnTItLVIqQ). We saw that the equations are a way to link the stress-energy tensor to the Einstein tensor representing the curvature of spacetime - in simple terms, how mass and energy warps spacetime. As it turns out, tensors are extremely interesting mathematical objects that can easily be represented by matrices! Linear algebra is a very useful topic to study for General Relativity.
Now I've mentioned the two coolest (in my opinion) examples above - but matrix algebra is useful in other areas of physics too. Fluid dynamics, classical mechanics, you name it, you'll likely find matrices there. So I'd recommend learning things like matrix multiplication, matrix inversion, solving simultaneous equations with matrices, and more. Anything to help you get a better grasp of the topic. Because if you come to advanced physics concepts with a solid mathematical grasp of matrices, then you'll be able to spend more time understanding the physical interpretations of the physics you are learning!
Thanks so much for watching this video! If you enjoyed it, please do like and subscribe. Check out my socials too!
Instagram - parthvlogs
Patreon - patreon.com/parthg
