……特征向量、Hermitian、酉矩阵（unitary），还有谱分解！没错，Halmos 的那本书就是入门级 Hilbert 空间。然后再看一些应用结合的内容，比如 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》。也许还可以花一个晚上看看 LINPACK 的文档。挑个周末找点乐子，快速刷一遍 Tom M. Apostol 的《Mathematical Analysis: A……》里关于高斯、……斯托克斯定理的部分……
…eigenvectors, Hermitian, unitary, and the spectral decomposition! Right, the Halmos book is baby Hilbert space. Then look at some applied connections, e.g., George E.\ Forsythe and Cleve B.\ Moler, {\it Computer Solution of Linear Algebraic Systems,\/} Maybe spend an evening on the documentation of LINPACK. Some weekend of great fun, take a fast pass through the Gauss, ..., Stokes theorem parts of Tom M.\ Apostol, {\it Mathematical Analysis: A…
……y^1) = b^1 + c^1 = b^1 + b - b^1 = b 当然，这里可以多做几步迭代。这个过程叫做“iterative improvement”（迭代改进）。这些以及更多内容都收录在 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs, 1967）中。比如，要密切关注“partial pivoting”（列主元消去）。小心 Ax = b 可能有解但解不唯一的情况。如果你的问题属于这种情况，……
…y^1) = b^1 + c^1 = b^1 + b - b^1 = b Of course, could do several steps of iteration here. This process is called 'iterative improvement'. This and more are in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. E.g., pay close attention to 'partial pivoting'. Beware of the fact that Ax = b may have a solution but not a unique solution. If this is the case in your problem,…
……---------------------------------------- 如果想认真搞线性代数中的数值计算，那就考虑下面这本书，或者能找到更好的也行：George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs, 1967）。======================================== 多元统计 我入门多元统计主要看的是 N. R. Draper 和 H. Smith 的《Applied Regression……
…---------------------------------------- If want to take numerical computations in linear algebra seriously, then consider the next book or something better if can find it George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. ======================================== Multivariate Statistics My main start with multivariate statistics was N. R. Draper and H. Smith, 'Applied Regression…
……Richard Bellman 的《Introduction to Matrix Analysis: Second Edition》。Bellman 以动态规划闻名。至于线性代数计算，可以考虑 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》，不过现在 Linpack 的资料可能是学习数值线性代数更好的起点。数值线性代数现在已经是一个发展成熟的专门领域，而 Linpack 资料可能……
…of Richard Bellman, Introduction to Matrix Analysis: Second Edition. Bellman was famous for dynamic programming. For computations in linear algebra, consider George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems although now the Linpack materials might be a better starting point for numerical linear algebra. Numerical linear algebra is now a well developed specialized field, and the Linpack materials might…
……与高斯消元法的联系！为什么？为了数值稳定性，高斯消元法应该强调仔细选择“主元”（pivot）元素，比如像 George E. Forsythe 和 Cleve B. Moler 在《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs）中所写的那样。而线性规划的 simplex algorithm（单纯形算法）没有这种自由或奢侈条件。因此，单纯形算法中的每次“迭代”仅仅是一次初等……
…the connection with Gauss elimination! Why? Gauss elimination, for numerical stability, should emphasize careful selection of the 'pivot' elements, e.g., as in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs. and the simplex algorithm of linear programming does not have that freedom or luxury. So, each 'iteration' in the simplex algorithm is just an application of elementary…
……版，Prentice-Hall, Englewood Cliffs, New Jersey, 1971。https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-k... Halmos 的《Finite Dimensional Vector Spaces》、George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》、Paul R. Halmos 的《Naive Set Theory》（Van Nostrand, Princeton, NJ, 1960）。虽然自这本书之后又有不少新进展，但它作为公理集合论的入门书写得太棒了。所以，即使是那些想要……
…Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-k... Halmos, Finite Dimensional Vector Spaces George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems Paul R. Halmos, Naive Set Theory, Van Nostrand, Princeton, NJ, 1960. More has been done since this book, but this book is a gorgeous introduction to axiomatic set theory. So, even people who want to…
……特征向量、Hermitian、酉矩阵（unitary），还有谱分解！没错，Halmos 的那本书就是入门级 Hilbert 空间。然后再看一些应用结合的内容，比如 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》。也许还可以花一个晚上看看 LINPACK 的文档。挑个周末找点乐子，快速刷一遍 Tom M. Apostol 的《Mathematical Analysis: A……》里关于高斯、……斯托克斯定理的部分……
…eigenvectors, Hermitian, unitary, and the spectral decomposition! Right, the Halmos book is baby Hilbert space. Then look at some applied connections, e.g., George E.\ Forsythe and Cleve B.\ Moler, {\it Computer Solution of Linear Algebraic Systems,\/} Maybe spend an evening on the documentation of LINPACK. Some weekend of great fun, take a fast pass through the Gauss, ..., Stokes theorem parts of Tom M.\ Apostol, {\it Mathematical Analysis: A…
……y^1) = b^1 + c^1 = b^1 + b - b^1 = b 当然，这里可以多做几步迭代。这个过程叫做“iterative improvement”（迭代改进）。这些以及更多内容都收录在 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs, 1967）中。比如，要密切关注“partial pivoting”（列主元消去）。小心 Ax = b 可能有解但解不唯一的情况。如果你的问题属于这种情况，……
…y^1) = b^1 + c^1 = b^1 + b - b^1 = b Of course, could do several steps of iteration here. This process is called 'iterative improvement'. This and more are in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. E.g., pay close attention to 'partial pivoting'. Beware of the fact that Ax = b may have a solution but not a unique solution. If this is the case in your problem,…
……---------------------------------------- 如果想认真搞线性代数中的数值计算，那就考虑下面这本书，或者能找到更好的也行：George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs, 1967）。======================================== 多元统计 我入门多元统计主要看的是 N. R. Draper 和 H. Smith 的《Applied Regression……
…---------------------------------------- If want to take numerical computations in linear algebra seriously, then consider the next book or something better if can find it George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs, 1967. ======================================== Multivariate Statistics My main start with multivariate statistics was N. R. Draper and H. Smith, 'Applied Regression…
……Richard Bellman 的《Introduction to Matrix Analysis: Second Edition》。Bellman 以动态规划闻名。至于线性代数计算，可以考虑 George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》，不过现在 Linpack 的资料可能是学习数值线性代数更好的起点。数值线性代数现在已经是一个发展成熟的专门领域，而 Linpack 资料可能……
…of Richard Bellman, Introduction to Matrix Analysis: Second Edition. Bellman was famous for dynamic programming. For computations in linear algebra, consider George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems although now the Linpack materials might be a better starting point for numerical linear algebra. Numerical linear algebra is now a well developed specialized field, and the Linpack materials might…
……与高斯消元法的联系！为什么？为了数值稳定性，高斯消元法应该强调仔细选择“主元”（pivot）元素，比如像 George E. Forsythe 和 Cleve B. Moler 在《Computer Solution of Linear Algebraic Systems》（Prentice-Hall, Englewood Cliffs）中所写的那样。而线性规划的 simplex algorithm（单纯形算法）没有这种自由或奢侈条件。因此，单纯形算法中的每次“迭代”仅仅是一次初等……
…the connection with Gauss elimination! Why? Gauss elimination, for numerical stability, should emphasize careful selection of the 'pivot' elements, e.g., as in George E. Forsythe and Cleve B. Moler, 'Computer Solution of Linear Algebraic Systems', Prentice-Hall, Englewood Cliffs. and the simplex algorithm of linear programming does not have that freedom or luxury. So, each 'iteration' in the simplex algorithm is just an application of elementary…
……版，Prentice-Hall, Englewood Cliffs, New Jersey, 1971。https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-k... Halmos 的《Finite Dimensional Vector Spaces》、George E. Forsythe 和 Cleve B. Moler 的《Computer Solution of Linear Algebraic Systems》、Paul R. Halmos 的《Naive Set Theory》（Van Nostrand, Princeton, NJ, 1960）。虽然自这本书之后又有不少新进展，但它作为公理集合论的入门书写得太棒了。所以，即使是那些想要……
…Edition, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-k... Halmos, Finite Dimensional Vector Spaces George E. Forsythe and Cleve B. Moler, Computer Solution of Linear Algebraic Systems Paul R. Halmos, Naive Set Theory, Van Nostrand, Princeton, NJ, 1960. More has been done since this book, but this book is a gorgeous introduction to axiomatic set theory. So, even people who want to…