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Vector Spaces and Matrices in Physics M C Jain PDF Download  Form

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It’s Professor Dave, let’s check out some spaces. We’ve talked a lot about vectors and matrices lately, as well as how certain mathematical operations like addition and scalar multiplication work on them. Now we want to generalize these operations to define what is known as a vector space, which is sometimes also called a linear space, so let’s look at this concept now. Before defining anything, let’s just introduce some notation. Let’s call our vector space V. If some vector is a member, or “element” of V, we can denote it with this symbol here, so the following means that A is an element of V. All elements of the vector space have the same properties we already discussed for vectors, so elements must abide by the commutative and associative properties of addition, as is shown here. There also exists a zero vector in the vector space such that any element plus the zero vector will just give back the element. For each element a, there exists another element, -a, within

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