## 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 x is a

related by equation (110) in which P is the transition matrix from the E- to the F-

basis. AriF> and /lr</0 have the same determinant. Thus det AJi:)\s independent

of ...

If x is a

**linear**operator in U, then the matrices of x relative to the two bases arerelated by equation (110) in which P is the transition matrix from the E- to the F-

basis. AriF> and /lr</0 have the same determinant. Thus det AJi:)\s independent

of ...

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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