Homogeneous functions (Banach)

Question

I am reading a textbook (on sectorial operators) and the author mentions that for a real Banach space $X$, the function $\phi:X\times X\rightarrow \mathbb{R};\phi(x_1,x_2)=(\|x_1\|^2+\|x_2\|^2)^{1/2}$, is, in general, not homogeneous. However we see that $$ \phi(tx_1,tx_2)=t^1\phi(x_1,x_2). $$

What does the author mean?

Answer 1

We have $\phi(tx_1,tx_2)=t\phi(x_1,x_2)$ only in the case $t \ge 0$.

In general we have

$\phi(tx_1,tx_2)=|t|\phi(x_1,x_2)$