The mapping set of all the elements in set A is called the mapping image set and marked as imA. Obviously, the image set of set A about mapping F can be expressed as imA=f(A).
The symbol of ker is a linear mapping, which is a linear mapping from the linear space V 1 on the number field K to V2, so the original image set of zero vector in V2 under A is kerA；; A's album is recorded as imA.
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Linear algebra is a successful theory and its method has been applied to other branches of mathematics.
1, modular theory is to use rings instead of scalar fields in linear algebra.
2. Multilinear algebra linearizes the "multivariable" problem of mapping into the problem of each different variable, thus generating the concept of tensor.
3. In the spectral theory of operators, the infinite dimensional matrix can be controlled by mathematical analysis.
Every linear space has a base. Yeah, one? n？ Okay？ n？ Non-zero matrix of column? A, if there is a matrix? b？ Manufacturing? AB？ =? Ba? =E(E is identity matrix), then? Answer? Is nonsingular matrix (or invertible matrix), and b is the inverse matrix of a.
A matrix is nonsingular (invertible) if and only if its determinant is not zero. A matrix is nonsingular if and only if the linear transformation it represents is automorphism. A matrix is semi-positive definite if and only if each eigenvalue is greater than or equal to zero.
A matrix is positive definite if and only if each eigenvalue is greater than zero. Cramer's rule for solving linear equations. Judge the relationship between augmented matrix and coefficient matrix of non-zero real root linear equations.
Baidu encyclopedia-linear algebra