# Spatial orthogonal and vector projection

Source: Internet
Author: User

4 Sub-spaces:

1. Row space, 0 space
2. Column space, a transpose of 0 space.

What is an orthogonal vector? The two vectors have an angle of 90 degrees.

Right angle means: X + y Gets the new vector = x + y

|x|^2 + |y|^2 = |x+y|^2

How to prove it?

X ' *x + y ' *y = (x+y) ' * (x+y)

= (x ' +y ') * (x+y)

=x*x ' + y*y ' +x ' *y+x*y '

launched X ' *y=0

So x is perpendicular to Y.

SubSpace, sub-space. SubSpace quadrature means that any vector in S is orthogonal to any vector in T.

The vertical walls and floors are not orthogonal, as they have a cross line. Two spaces if orthogonal, only intersect at 0 points. So the line space and the 0 space are orthogonal. Because Ax=0, where a is a row space, X is a vector of 0 space.

And the number of their bases is exactly equal to N, so they are complementary.

-----------

Let's look at two orthogonal examples of two vectors:

Where A and B are two vectors, X is a number, and x*a is a projection of B on a.

Can get a ' * (b–x * a) = 0

And then get a ' *b–a ' *x*a=0 because x is constant, so

A ' * b = a ' *a*x

Both sides multiply 1/a *1/a ', noticing that the order of a and a ' is reversed.

Get x = A ' *b/(A*a ').

Spatial orthogonal and vector projection

Related Keywords:

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

## A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

• #### Sales Support

1 on 1 presale consultation

• #### After-Sales Support

24/7 Technical Support 6 Free Tickets per Quarter Faster Response

• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.