The problem with Linear Algebra specifically, is that it can be viewed from many different perspectives.
The article here focuses on an "operational" perspective, how the numbers get added or multiplied together to turn into other numbers. However, Linear Algebra is also useful in geometry, and other situations.
This "intuitive guide" to linear algebra sets you up very nicely for figuring out how to add and multiply matricies together. But it doesn't give you any intuition about a rotation (aka quaternions) in 3d space, for example. A lot of math books make the mistake of trying to teach all the perspectives at the same time, instead of focusing on just one viewpoint until the student gains mastery.
A Quaternion is "just" a 4x4 matrix that represents rotation in 3-dimension space. Because you only move 3-ways rotationally (yaw, pitch, and roll), you're "underconstrained" with regards to the 4x4 matrix. Etc. etc. A lot of geometry intuition needs to be built here to really understand Quaternion... and none of that geometry is explored in the blogpost.
Which is fine. Focus is good. But when people approach Linear Algebra, its important to know that its "so useful" that there are too many ways of looking at Linear Algebra... too many different, yet equivalent, understandings of the subject.
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The problem with Linear Algebra specifically, is that it can be viewed from many different perspectives.
The article here focuses on an "operational" perspective, how the numbers get added or multiplied together to turn into other numbers. However, Linear Algebra is also useful in geometry, and other situations.
This "intuitive guide" to linear algebra sets you up very nicely for figuring out how to add and multiply matricies together. But it doesn't give you any intuition about a rotation (aka quaternions) in 3d space, for example. A lot of math books make the mistake of trying to teach all the perspectives at the same time, instead of focusing on just one viewpoint until the student gains mastery.
A Quaternion is "just" a 4x4 matrix that represents rotation in 3-dimension space. Because you only move 3-ways rotationally (yaw, pitch, and roll), you're "underconstrained" with regards to the 4x4 matrix. Etc. etc. A lot of geometry intuition needs to be built here to really understand Quaternion... and none of that geometry is explored in the blogpost.
Which is fine. Focus is good. But when people approach Linear Algebra, its important to know that its "so useful" that there are too many ways of looking at Linear Algebra... too many different, yet equivalent, understandings of the subject.