It’s a vector space inside a vector space. (Similarly, the vector a v is an element of the set V ).Īnd there’s another important concept called “ subspace”, sometimes referred to as “linear subspace”. : F × V → V, takes any scalar a and any vector v and gives another vector a v.The second operation, called scalar multiplication.(Note that the resultant vector is also an element of the set V ). The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and wand assigns to them a third vector which is commonly written as v + w, and called the sum of these two vectors.Like in the example above, the vector space must satisfy vector addition (like when we added two vectors to get the outcome) and multiplication by a scalar (like when we multiplied the 1st column vector with a scalar 2) and stay in the same vector space. My purpose here is to provide you with enough details to understand the key concepts from his lectures so that you could gain the most out of it with the smallest amount of time. It’s a very good lecture and I strongly advise you to watch all the videos. In this series “Towards understanding Linear Algebra”, I’m going to cover topics based on famous and excellent lectures by Dr. Digital Signal Processing, State-space estimation, Machine Learning, Deep Learning, etc.). I’m particularly interested in Brain Computer Interface (BCI) and many fields composing the field use Linear Algebra as a basis (e.g. Linear Algebra is one of the fundamental topics that you should be very comfortable with. Then you might need to go back again to learn the fundamentals before going back to learn the most exciting advanced materials which could be time consuming. If you put more things on top of the weak basis, it could break apart in the end, meaning you end up not fully understanding any of the materials you learned. Why? Because the fundamentals are the basis where you build your advanced knowledge on top of. I believe understanding fundamental concepts is crucial when it comes to learning something advanced.
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