Mike's lecture on vector spaces and dual spaces: Difference between revisions
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=LECTURE 1: Vector Spaces and Dual Spaces= | =LECTURE 1: Vector Spaces and Dual Spaces= | ||
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[[#ref1]][1] - Note that some have raised technical concerns about this operation being called the "dot product," insisting that the dot product is something that's only done between two vectors, or two covectors, but never between one covector and one vector. Another term that's sometimes been used for this product in the "**bracket product**", for reasons we don't need to get into here. However, confusingly, the term bracket product has also been used for the ordinary dot product, and it's also very common to hear people call the thing I'm calling the dot product above. It's best at this point to just know that the two terms are out there. I'm going to continue calling it the dot product since its' something more people are familiar with.</pre></div> | [[#ref1]][1] - Note that some have raised technical concerns about this operation being called the "dot product," insisting that the dot product is something that's only done between two vectors, or two covectors, but never between one covector and one vector. Another term that's sometimes been used for this product in the "**bracket product**", for reasons we don't need to get into here. However, confusingly, the term bracket product has also been used for the ordinary dot product, and it's also very common to hear people call the thing I'm calling the dot product above. It's best at this point to just know that the two terms are out there. I'm going to continue calling it the dot product since its' something more people are familiar with.</pre></div> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc1"><a name="LECTURE 1: Vector Spaces and Dual Spaces"></a><!-- ws:end:WikiTextHeadingRule:6 -->LECTURE 1: Vector Spaces and Dual Spaces</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc1"><a name="LECTURE 1: Vector Spaces and Dual Spaces"></a><!-- ws:end:WikiTextHeadingRule:6 -->LECTURE 1: Vector Spaces and Dual Spaces</h1> | ||