Introduction to Linear Algebra (Chapter2)

Chapter 2 Solving Linear equations

2.1 Vectors and Linear equations

the core problem of linear algebra : Solving the equation system. ------------"but slope are important in calculus and this islinear algebra".

a*x=b two kinds of viewpoints: The line space of a and the inner product of x, or a linear combination of the column spaces of a. -------key Issue

Common matrix decomposition : LU, QR, SVD (most commonly used).

2.2 The idea of elimination

elimination Method : The upper triangular matrix is produced. ------------ Line interchange, line subtraction

2.3 Matrix Eliminating Element method

Left row right column matrix Exchange matrix

2.4 Matrix Operations

The addition, multiplication, multiply of matrices.

three kinds of viewpoint of matrix multiplication: The inner product of row-column vectors, the outer product of column-line vectors, and the superposition of line-line vectors. --------------- the inner product and outer product of the vector. The inner product produces the scalar, the outer product produces the matrix

Chunking Matrix:

2.5 Inverse matrix

How to judge the matrix reversible

Calculation of inverse matrices: Gaussian elimination element method

2.6 lu Decomposition = = extinction element

matrix decomposition : Decomposition of matrix A into the product of two or three matrices (LU, QR, SVD)

LU decomposition : Using the Gaussian elimination method to get the U matrix, the inverse matrix of the matrix is L; The U matrix can continue to decompose to get the du matrix. -------------a=lu or A=ldu. Upper triangular matrix and lower triangular matrix

Solving linear equations by eliminating the element method: Ax=b

2.7 Transpose and displace

"I think the world was governed by linear algebra and physics disguises it well."

Many scientific computational problems, starting with the Matrix R, end with RTR or RRT.

The inverse of the permutation matrix equals the transpose of the permutation matrix

Introduction to Linear Algebra (Chapter2)