Linear Algebra | Lecture 7 (held online) скачать в хорошем качестве

Linear Algebra | Lecture 7 (held online)

(Held online, on Teams) Ch 2 resumed, continued with §2.3 Bases and Dimension, reviewed the definition of linearly independent sets, looked at a few consequences, then using that, introduced the definition of a basis, did a few examples (including an example with infinite basis) but skipped Example 15 (will give as an exercise in the assignment), proved Theorem 4 (linearly independent vectors cannot be more than the dimension of the space), looked at Corollary 1 (any two bases have the same number of elements), used this to forrmally define dimension, then did corollary 2 (restatement essentially of Theorem 4, using dimensions), Covered a few examples tot illustrate standard basis, proved a technical lemma (it was about adding a vector β∉span(S) to the basis of S where S is linearly independent subset of V; basically β∪S is still linearly independent). For lecture notes and other resources: https://donkeydocs.github.io/