What is the difference between zero-rank tensor $x$ (scalar) and vector $[x]$ in 1D?

As far as I understand tensor is anything which can be measured and different measures can be transformed into each other. That is, there are different basises for looking at one object.

Is length a scalar (zero rank tensor)? I think it is not. ex.:

• physical parameter: writing pen's length
• tensor: $l$
• length in inches: $[5.511811023622]$
• length in centimeters: $[14]$
• transformation law: 1cm = 2.54inch

so $l$ is a scalar, but on the other hand it's a tensor of rank 1 since "physical parameter of length is invariant, only it's measures (in different units) are".

The same example can be made with classical example of temperature (which is used as a primer of zero rank tensor most in any book) in C and K units. I'm confused.

What is the difference between zero-rank tensor $x$ (scalar) and vector $[x]$ in 1D?

As far as I understand tensor is anything which can be measured and different measures can be transformed into each other. That is, there are different basises for looking at one object.

Is length a scalar (zero rank tensor) or is it a 1D vector (rank 1 tensor)?

In books it is said that temperature, pressure and other "numbers" are 0rank tensors, they are invariant under transformations and posess no "direction" (that is there is no basis for them). But I'm cofused about units... I thinks of units as somekind of basis.

ex.:

• physical parameter: writing pen's length
• tensor: $l$
• length in "inches basis": $[5.511811023622]$
• length in "centimeters basis": $[14]$
• transformation law: 1cm = 2.54inch

so $l$ is a scalar (0rank), but on the other hand it's a vector (1rank).

The same logic can be applied to mutate classical examples of 0rank tensors: pressure, temperature (which is used as a primer of zero rank tensor most in any book) in C and K units. I'm confused.

What is the difference between zero-rank tensor $x$ (scalar) and 1D vector $[x]$?

As far as I understand tensor is anything which can be measured and different measures can be transformed into eachother. That is, there are different basises for looking at one object.

Is lengh a scalar (zero rank tensor)? I think it is not. ex.:

• physical parameter: writing pen's length
• tensor: $l$
• length in inches: $[5.511811023622]$
• length in centimeters: $[14]$
• transformation law: 1cm = 2.54inch

so $l$ is a scalar, but on the other hand it's a tensor of rank 1 since "physical parameter of length is invariant, only it's measures (in different units) are".

The same example can be made with classical example of temperature (which is used as a primer of zero rank tensor most in any book) in C and K units. I'm confused.

What is the difference between zero-rank tensor $x$ (scalar) and vector $[x]$ in 1D?

As far as I understand tensor is anything which can be measured and different measures can be transformed into each other. That is, there are different basises for looking at one object.

Is length a scalar (zero rank tensor)? I think it is not. ex.:

• physical parameter: writing pen's length
• tensor: $l$
• length in inches: $[5.511811023622]$
• length in centimeters: $[14]$
• transformation law: 1cm = 2.54inch

so $l$ is a scalar, but on the other hand it's a tensor of rank 1 since "physical parameter of length is invariant, only it's measures (in different units) are".

The same example can be made with classical example of temperature (which is used as a primer of zero rank tensor most in any book) in C and K units. I'm confused.