tag:blogger.com,1999:blog-5303307482158922565.post7841318941683305336..comments2024-03-22T13:39:55.941-07:00Comments on Math Mama Writes...: Linkfest for Friday, February 6Sue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5303307482158922565.post-1358656186787352162015-03-14T14:33:41.586-07:002015-03-14T14:33:41.586-07:00Nice! (I Knew linear connected to keeping vector s...Nice! (I Knew linear connected to keeping vector space properties, but you put it well. And thinking about "normalizing", by using z-score to equate the mean with z=0, makes it clear why you'd want that broader definition in statistics.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-6795272406965219532015-03-14T08:19:01.484-07:002015-03-14T08:19:01.484-07:00Did you get your question answered about linear vs...Did you get your question answered about linear vs affine transformations and "math linear" vs "stats linear?" If not, here are some quick points:<br /><br />One key point in reconciling the stats and linear algebra definitions is that, with one important exception, key statistics are calculated relative to the distribution mean. The exception is the mean itself. This implies that other statistics, standard deviation, skewness, kurtosis, correlation, etc, are not affected when you add a constant. Further, that means most of the time statisticians move into a world where means are uniformly 0 and linear transformations are the same as in linear algebra.<br /><br />Now, why exclude X -> aX + b in linear algebra? Actually, these are called affine transformations and do have their own limelight of study. However, one (modern?) way of thinking is that linear transformations are the maps between vector spaces that preserve the vector space properties, thus are a natural place to focus.JGR314https://www.blogger.com/profile/11702319994021721608noreply@blogger.com