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>I'm half-convinced that the “rank of a matrix” is just an artefact ... The rank of a matrix is fundamental to understanding linear transformations, since it g

>I'm half-convinced that the “rank of a matrix” is just an artefact ... The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". It becomes more fundamental if the person goes on to study deeper math. It tells you how to compute the size of a basis for the target space. The uses go on and on. >And distributions aren't everything; I can look up any distribution I want on Wikipedia Yes, you can look up anything on wikipedia, but not in this book, which is why this book will not teach you the things the OP claimed it would. >a proper foundation in what statistics means is much harder to come by It's very hard to get that proper foundation from a book that does not cover those foundations. One is better served by using a proper book with a consistent and well laid out presentation of the needed concepts. Saying one can look fundamental stuff up elsewhere means the book is lacking.

wizzwizz4 5y ago
> The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". That's more to do with the space of the coefficients, I think. > Saying one can look fundamental stuff up elsewhere means the book is lacking. A list of distributions is not fundamental to statistics. Discovering a new distribution doesn't meaningfully expand the fundamentals of the field of statistics: all the basic principles are the same. Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distributions when they're needed.
- ChrisLomont 5y ago
  >That's more to do with the space of the coefficients, I think. I don't think that phrase is a thing in linear algebra. I've gotten a PhD in mathematics - I know both these fields quite well. I stand by my assessment of linear algebra - I've been using pieces form it nearly daily for decades. >Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distributions when they're needed. And a student trying to learn where and why stats is useful should be taught a wide set of distributions so they see the nuances while they're learning. Sure, you can provide only a Gaussian, but when the student leaves completely ignorant of all the places a gaussian fails and what are some choices relevant to different situations, you can failed to teach them the fundamentals, which includes enough nuance to see when and where to apply what distribution. >A list of distributions is not fundamental to statistics. You may as well claim all of stats is not fundamental - just learn math principles. You can look up anything in stats and derive it yourself once given the concept if you're good at math fundamentals. Surely with enough math skills, and zero stats, you can derive all the stats knowledge needed without needing to ever see any stats in a book. But that's a bad way to go about teaching people useful skills. A student learning about distributions needs some examples. This book has none. You can argue all you want, but this book is crap for learning the topics the OP claimed it covers. Find a textbook for beginning students that does not cover a multitude of distributions. Either every single author, usually writing from decades of experience, is wrong, or you are. I think the authors have the right approach.
  - wizzwizz4 5y ago
    > I don't think that phrase is a thing in linear algebra. You're right; sorry for the typo. I meant the span of the coefficients (which is a space). I'm not saying the concept of “rank” is useless, or anything. I'm saying a lot of linear algebra is based on high-level techniques and algorithms, but I don't think they're not truly fundamental concepts that you need to learn to understand linear algebra, if you learn / intuit a different high-level formulation instead. > And a student trying to learn where and why stats is useful That's not what I mean by “fundamentals”: I mean what stats is and how it works. A solid grounding in applied statistics is just as much about human psychology as it is about mathematics, and you never need know where your distributions come from so long as you memorise the rules. > Sure, you can provide only a Gaussian, Is that what the book does? If so, then I completely agree. But I don't see why you can't teach statistics using a Gaussian, a Poisson, a beta (three arbitrary distributions) and a general “some distribution”. I'm more of a pure mathematician, though, so if the answer's just “that doesn't prepare statisticians well for the kind of distributions that come up in the real world” then I can well believe it. > Find a textbook for beginning students that does not cover a multitude of distributions. … Aren't we discussing one?
    - ChrisLomont 5y ago
      >but I don't think they're not truly fundamental concepts that you need to learn to understand linear algebra I'd argue that without a deep understanding of rank and nullity you do not understand linear algebra. Sure, you can lean to move symbols and compute simple things, but that is not much of an understanding. I'd guess you have not moved into deeper things - then you'll realize you're missing fundamental understanding of linear algebra needed to move on. It's like claiming one has a fundamental understanding of calculus by being able to solve high school level integrals, but really doesn't understand deep relations between the main ideas of calculus. Sure you can write things down, but there is a major difference between that level of knowledge and what I'd call a fundamental understanding of calculus. >span of the coefficients ???? Care to link to the thing you're misnaming? I have no idea what you're talking about, and I even googled the phrase. This is what I mean by using a proper book to learn from. >Aren't we discussing one? Nope - the book in question is not offered as a beginner course stats anywhere I am aware of. Care to show one? Calling it one then claiming it is evidence of one is simply circular logic. >Is that what the book does? So you have not looked at the book yet are arguing what kind of book it is? That about sums this up.

wizzwizz4 5y ago

> The rank of a matrix is fundamental to understanding linear transformations, since it given you knowledge about the dimensions of the "output space". That's more to do with the space of the coefficients, I think. > Saying one can look fundamental stuff up elsewhere means the book is lacking. A list of distributions is not fundamental to statistics. Discovering a new distribution doesn't meaningfully expand the fundamentals of the field of statistics: all the basic principles are the same. Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distributions when they're needed.

ChrisLomont 5y ago
>That's more to do with the space of the coefficients, I think. I don't think that phrase is a thing in linear algebra. I've gotten a PhD in mathematics - I know both these fields quite well. I stand by my assessment of linear algebra - I've been using pieces form it nearly daily for decades. >Anyone familiar with those basic principles can pick up a new distribution quite easily – and can probably derive new distributions when they're needed. And a student trying to learn where and why stats is useful should be taught a wide set of distributions so they see the nuances while they're learning. Sure, you can provide only a Gaussian, but when the student leaves completely ignorant of all the places a gaussian fails and what are some choices relevant to different situations, you can failed to teach them the fundamentals, which includes enough nuance to see when and where to apply what distribution. >A list of distributions is not fundamental to statistics. You may as well claim all of stats is not fundamental - just learn math principles. You can look up anything in stats and derive it yourself once given the concept if you're good at math fundamentals. Surely with enough math skills, and zero stats, you can derive all the stats knowledge needed without needing to ever see any stats in a book. But that's a bad way to go about teaching people useful skills. A student learning about distributions needs some examples. This book has none. You can argue all you want, but this book is crap for learning the topics the OP claimed it covers. Find a textbook for beginning students that does not cover a multitude of distributions. Either every single author, usually writing from decades of experience, is wrong, or you are. I think the authors have the right approach.
- wizzwizz4 5y ago
  > I don't think that phrase is a thing in linear algebra. You're right; sorry for the typo. I meant the span of the coefficients (which is a space). I'm not saying the concept of “rank” is useless, or anything. I'm saying a lot of linear algebra is based on high-level techniques and algorithms, but I don't think they're not truly fundamental concepts that you need to learn to understand linear algebra, if you learn / intuit a different high-level formulation instead. > And a student trying to learn where and why stats is useful That's not what I mean by “fundamentals”: I mean what stats is and how it works. A solid grounding in applied statistics is just as much about human psychology as it is about mathematics, and you never need know where your distributions come from so long as you memorise the rules. > Sure, you can provide only a Gaussian, Is that what the book does? If so, then I completely agree. But I don't see why you can't teach statistics using a Gaussian, a Poisson, a beta (three arbitrary distributions) and a general “some distribution”. I'm more of a pure mathematician, though, so if the answer's just “that doesn't prepare statisticians well for the kind of distributions that come up in the real world” then I can well believe it. > Find a textbook for beginning students that does not cover a multitude of distributions. … Aren't we discussing one?
  - ChrisLomont 5y ago
    >but I don't think they're not truly fundamental concepts that you need to learn to understand linear algebra I'd argue that without a deep understanding of rank and nullity you do not understand linear algebra. Sure, you can lean to move symbols and compute simple things, but that is not much of an understanding. I'd guess you have not moved into deeper things - then you'll realize you're missing fundamental understanding of linear algebra needed to move on. It's like claiming one has a fundamental understanding of calculus by being able to solve high school level integrals, but really doesn't understand deep relations between the main ideas of calculus. Sure you can write things down, but there is a major difference between that level of knowledge and what I'd call a fundamental understanding of calculus. >span of the coefficients ???? Care to link to the thing you're misnaming? I have no idea what you're talking about, and I even googled the phrase. This is what I mean by using a proper book to learn from. >Aren't we discussing one? Nope - the book in question is not offered as a beginner course stats anywhere I am aware of. Care to show one? Calling it one then claiming it is evidence of one is simply circular logic. >Is that what the book does? So you have not looked at the book yet are arguing what kind of book it is? That about sums this up.