线性代数第5版Gilbertstrang吉尔伯特英文版PDF及课后答案

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线性代数第5版Gilbertstrang吉尔伯特英文版PDF及课后答案资料导读

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The cover shows the Four Fundamental Subspaces-the row space and nullspace are on the left side, the column space and the nullspace of AT are on the right. It is not usual to put the central ideas of the subject on display like this! When you meet those four spaces in Chapter 3, you will understand why that picture is so central to linear algebra.

Those were named the Four Fundamental Subspaces in my first book, and they start from a matrix A. Each row of A is a vector in n-dimensional space. When the matrix has m rows, each column is a vector in m-dimensional space. The crucial operation in linear algebra is to take linear combinations ofcolumn vectors. This is exactly the result of a matrix-vector multiplication. Ax is a combination of the columns of A.

When we take all combinations Ax of the column vectors, we get the column space.If this space includes the vector b, we can solve the equation Ax = b.