Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.

User Guide

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
think,
figure-out, &
learn.

Just keep tapping (or clicking) on the content to continue in the trail and learn.

User Guide

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

User Guide

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about.

User Guide

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step.

User Guide

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen.

User Guide

exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge.

summary of this topic

### Properties of Dot Product

Voice

Voice

Home

»  vector dot product is bilinear
→  vec p cdot (lambda vec q + vec r)   = lambda (vec p cdot vec q)   + vec p cdot vec r

### Bilinear Property

plain and simple summary

nub

plain and simple summary

nub

dummy

•  Dot product is bilinear.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

Support Nubtrek

You are learning the free content, however do shake hands with a coffee to show appreciation.
To stop this message from appearing, please choose an option and make a payment.

Keep tapping on the content to continue learning.
Starting on learning "Bilinear Property of vector dot product". ;;

Dot product is defined between vec p, vec q in bbb V and the result vec p cdot vec q in RR. This can be considered as a transformation. What type of transformation is this?

• unary
• binary
• ternary

The answer is 'binary', as the input is two vectors. 'bi' means two.

Which of the following property is true for Bilinear transformation?

• T(x+y, z)=T(x,z)+T(y,z)
• T(ax,z)=aT(x,z)
• T(ax+y, z)= aT(x,z)+T(y,z)
• All the above

The answer is 'All the above'.

This property defines linearity for binary operator T. That is why it is named Bilinear.

Consider the dot product as a binary transform T(vec p, vec q) = vec p cdot vec q. Is dot product bilinear?

• Yes
• No

The answer is 'Yes'. The dot product is distributive over vector addition and also satisfies the scalar multiple property.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Bilinear Property: For any vector vec p, vec q, vec r in bbb V and lambda in RR
(lambda vec p + vec q) cdot vec r = lambda (vec p cdot vec r) + (vec q cdot vec r)

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

Given vec x cdot vec z = 2 and vec y cdot vec z = 1, what is (3 vec x + 2 vec y) cdot vec z?

• 5
• 6
• 8
• 9

The answer is '8'
(3 vec x + 2 vec y) cdot vec z
quad = 3 vec x cdot vec z + 2 vec y cdot vec z

Progress

Progress

Dot product is defined between vector p and q in vector space v. And the result vector p dot vector q in real numbers. This can be considered as a transformation. What type of transformation is this?
unary
unary
binary
binary
ternary
ternary
The answer is "binary", as the input is two vectors. bi means two.
Which of the following property is true for Bilinear transformation?
1
2
3
4
The answer is "All the above". This property defines linearity for a binary operator T. That is why it is names bilinear.
Consider the dot product as a binary transform : t of vector p, vector q =, vector p dot vector q. Is dot product bilinear?
yes;s
Yes
no
No
The answer is 'Yes'. The dot product is distributive over vector addition and also satisfies the scalar multiple property.
Dot product is bilinear.
Bilinear Property: For any vector p, q, r in vector space v, and lambda in real numbers. lambda times vector p plus vector q, dot vector r =, lambda times vector p dot vector r ,+, vector q dot vector r.
Given vector x dot vector z = 2 and vector y dot vector z = 1, what is 3 times vector x plus 2 times vector y, dot vector z?
1
2
3
4