《Introduction to Linear Algebra, Fourth Edition》的原文摘录
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we needed to open linear algebra to the world (查看原文) —— 引自第1页 -
Let me connect these special matrices A and S to calculus. The vector x changes to a function x(t). The differences Ax become the derivative dx/ dt = bet). In the inverse direction, the sum Sb becomes the integral of bet). (查看原文) —— 引自第24页 -
When E multiplies on the right, it acts on the columns of A. (查看原文) —— 引自第59页 -
Schur complement. (查看原文) —— 引自第72页 -
To solve A x = b without A-I, we deal with one column b to find one column x. (查看原文) —— 引自第85页 -
Suppose there is a nonzero vector x such that Ax = 0 (查看原文) —— 引自第81页 -
A triangular matrix is invertible if and only if no diagonal entries are zero. (查看原文) —— 引自第86页 -
The column space C (U) consists of all vectors of the form (b I , b2 , b3 , 0). (查看原文) —— 引自第137页 -
The same column of A can't be a combination of earlier columns, because Ax = 0 exactly when Rx = O. (查看原文) —— 引自第146页 -
The square matrix AT A is invertible when the rank is n (查看原文) —— 引自第157页 -
My choice for Xp would be (1,0). (查看原文) —— 引自第161页 -
The point is, our definition doesn't pick out one particular vector as gUilty. All columns of A are treated the same (查看原文) —— 引自第171页 -
This V is the nullspace of any m by 3 matrix B of rank 1, if every row is a multiple of (0, 0,1). (查看原文) —— 引自第177页 -
The pivot columns of A are a basis for its column space... (查看原文) —— 引自第173页 -
recursive least squares (查看原文) —— 引自第213页 -
Then ATA, with this same nullspace, is invertible. (查看原文) —— 引自第211页 -
You may think that projection onto the whole space is not worth mentioning. (查看原文) —— 引自第233页
作者: Gilbert Strang
isbn: 0980232716
书名: Introduction to Linear Algebra, Fourth Edition
页数: 584
定价: USD 87.50
出版社: Wellesley-Cambridge Press
出版年: 2009-2-10
装帧: Hardcover