I am reading Bruce N. Coopersteins book: Advanced Linear Algebra (Second Edition) ... ...(adsbygoogle = window.adsbygoogle || []).push({});

I am focused on Section 10.3 The Tensor Algebra ... ...

I need help in order to get a basic understanding of Definition 10.5 in Section 10.3 ...

Definition 10.5 plus some preliminary definitions reads as follows:

In the above text from Cooperstein, in Definition 10.5, we read the following:

" ... ... An element ##x \in \mathcal{T}(V)## is said to be homogeneous of degree ##d## if ##x \in \mathcal{T}_d (V)## ... ..."

My question is as follows:

How can x be such that ##x \in \mathcal{T}(V)## and ##x \in \mathcal{T}_d (V)## ... does not seem possible to me ... ...

... ... because ... ...

... if ##x \in \mathcal{T}(V)## then ##x## will have the form of an infinite sequence as in the following:

##x = (x_0, x_1, x_2, \ ... \ ... \ , x_{d-1}, x_d, x_{d+1}, \ ... \ ... \ ... \ ... ) ##

where ##x_i \in \mathcal{T}_i (V)##

... ... clearly ##x_d## is the ##d##-th coordinate of ##x## and so cannot be equal to ##x## ... ..

Can someone please clarify this issue ... clearly I am not understanding this definition ...

Peter

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I The Tensor Algebra - Cooperstein, Defn 10.5

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**