LATENT ROOTS AND VECTORS
(/;) Reconstruction,

493

x

| ^

h

~...*^1              o
v'H

| I              2
ft | _v 14      V*
| I
p* | O
| 2              I
Pi | _ 7»+   \^xf>

_x

x
/a

v«
0

^/^

M*
?i
* abilities*^1 (Note the somewhat questionable assumption, clearly
brought out by the table, that for the same test each testee employs
precisely the same abilities in precisely the same proportions,)
The unit hierarchies have a number of peculiar properties, which
render this mode of analysis particularly convenient for mathe-
matical manipulation and which the reader can easily verify in the
present instance ; they are * idempotent/ i.e. JEf = E$; they are
mutually orthogonal, Le* Mi J£j « o ,* their sum is equal to the unit
matrix* ie» JS^ •+• . * , + J£» =« I; and the ^f trace' of each (sum
of diagonal elements)« I, (Of. [115], 'The Unit Hierarchy and
Its Properties*')