# Canonical form derivation of (L1'AL1)

• I
• Sanchayan Ghosh
In summary, the conversation discusses the understanding of the equation L'AL = Λ and the reason for taking γΛγ1 = Σy2λ = 1. The person also mentions resolving a problem with a blurred picture and explains that y'Δy is the result of multiplying the transpose of vector components of y with a symmetric matrix Δ. The conversation ends with a thank you.

#### Sanchayan Ghosh

Hello everyone,

I actually had a problem with understanding the part where they have defined L'AL = Λ. There, they have taken
γΛγ1 = Σy2λ = 1. Why have they taken that? Is it arbitary or does it come as a result of a derivation?

Thank you

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sorry, we cannot see the picture

I don't know why it got blurred. Actually I resolved the problem.
y'Δy is nothing but mitiplying the transpose of vector components of y with the symmetric matrix
Δ = L'1AL1
L is the 1x3 matrix of eigen values of a symmetric matrix A.
And then multiplying the result with y vector. This gives the above expression as I had asked.

Thank you.

## 1. What is the purpose of deriving the canonical form of L1'AL1?

The canonical form of L1'AL1 is derived in order to simplify and standardize the representation of the language, making it easier to analyze and understand. It also allows for easier comparison and combination with other languages.

## 2. How is the canonical form of L1'AL1 derived?

The canonical form of L1'AL1 is derived using a series of transformations, such as removing duplicate symbols and simplifying expressions, until a unique and simplified form is obtained.

## 3. What are the benefits of using the canonical form of L1'AL1?

Using the canonical form of L1'AL1 allows for easier analysis and manipulation of the language, as well as making it more compatible with other languages. It also helps to identify patterns and similarities within the language.

## 4. Can the canonical form of L1'AL1 be derived for any language?

Yes, the canonical form can be derived for any language, as long as it follows a well-defined grammar and syntax.

## 5. How does the canonical form of L1'AL1 differ from other forms of representation?

The canonical form of L1'AL1 is unique and simplified, while other forms of representation may vary depending on the context and purpose. It also allows for easier comparison and analysis of the language.