## Orthogonal complement

Orthogonal complement is defined as subspace $M^\perp = \{ v\in V\,|\, \langle v, m\rangle = 0,\forall m\in M\}$. This is really a subspace because of linearity of scalar product

Explain mathematic questions

Math can be a difficult subject for some students, but with a little patience and practice, it can be mastered.

Explain math question

Math is the study of numbers, shapes, and patterns.

Build brilliant future aspects

You can build a bright future for yourself by taking advantage of the resources and opportunities available to you.

## 6.2: Orthogonal Complements

Finding the orthogonal complement of a span? Let V = P3(R) the vector space of all polynomials in t of degree at most 3. W = M2 × 2(R) the vector space of all 2 × 2 real matrices.

## Our students love us

Online school sent me my math 3 weeks late, and i got a bad start. Fun and an easy to use tool to work out maths questions, awsome app ive been having troubble in math and this only takes one photo. It does all the maths correctly. 5 out of 5. It is really useful for those students who are weak in maths and couldn't arrange a tutor.

Hilario Chan

This is a really great app in which I can solve and understand how to solve complicated math sums. This app as helped me alot. I like this application that's why I'm giving it 5 star. This is a very good app, it helps me a lot but there's some problem like I can't find the topic for my question.

Tommy Milner

• Solve equation

Try to find the answer to the equation.

• Clear up mathematic equation

Mathematics is the language of the universe, and equations are its grammar.

• Homework Support Online

Looking for a little help with your homework? Check out our solutions for all your homework help needs!

## Orthogonal Complements

Span{e1, e2} ⊥ = {(x y z w) in R|(x y z w) ⋅ (1 0 0 0) = 0 and (x y z w)(0 1 0 0) = 0} = {(0 0 z w) in R4} = Span{e3, e4}: the orthogonal complement of the xy -plane is the zw -plane.

• 515 Math Experts