Schmidt's orthogonal memory formula is: one-axis contraction, two-axis return, two-axis expansion, third-axis change, size contraction, direction change and size return.
Schmidt orthogonalization is a common method in linear algebra, which is used to transform a group of linearly independent vectors into orthogonal bases.
What is Schmidt orthogonalization?
For n-order matrices, if the eigenvectors of the same eigenvalue are not orthogonal, Schmidt orthogonalization is needed to make them orthogonal.
Schmidt orthogonalization is a method to find orthogonal bases in Euclidean space. Starting from vector group α 1, α2, ..., αm linearly independent of Euclidean space, orthogonal vector group β 1, β2, ..., βm is obtained, so that α 1, α2, ..., αm and vector group β 1, β2.
Linear algebra:
Linear algebra is a branch of mathematics, and its research objects are vectors, vector spaces (or linear spaces), linear transformations and linear equations with finite dimensions. Vector space is an important subject in modern mathematics. Therefore, linear algebra is widely used in abstract algebra and functional analysis; Through analytic geometry, linear algebra can be expressed concretely.
The theory of linear algebra has been extended to operator theory. Because the nonlinear model in scientific research can usually be approximated as a linear model, linear algebra is widely used in natural science and social science.