## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 263

of U, the set 6 of all

the subspace spanned by the set $). It is the smallest subspace of U containing

all vectors in $). The set 5) may be finite or infinite, but a

of U, the set 6 of all

**linear**combinations of vectors in S) is a subspace of U, calledthe subspace spanned by the set $). It is the smallest subspace of U containing

all vectors in $). The set 5) may be finite or infinite, but a

**linear**combination (see ...Page 264

If o- and r are both

in 11. ... in which n is the number of unknowns and r = rank A. A

transformation is one-to-one (that is, tV, = t\\ implies V, = V2) if, and only if, its

nullspace is 0.

If o- and r are both

**linear**operators in U tnen t<t and or are also**linear**operatorsin 11. ... in which n is the number of unknowns and r = rank A. A

**linear**transformation is one-to-one (that is, tV, = t\\ implies V, = V2) if, and only if, its

nullspace is 0.

Page 516

GEOMETRIC PRINCIPLES; ANALYSIS OF

noted,

between addition of functions and addition of vectors in two, three, and more ...

GEOMETRIC PRINCIPLES; ANALYSIS OF

**LINEAR**OPERATORS As alreadynoted,

**linear**functional analysis aims to exploit the formal similarity that existsbetween addition of functions and addition of vectors in two, three, and more ...

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