Column space
The column space of an m-by-n matrix with real entries is the subspace of Rm generated by the column vectors of the matrix. Its dimension is the rank of the matrix and is at most min(m,n).If one considers the matrix as a linear transformation from Rn to Rm, then the column space of the matrix equals the image of this linear transformation.
The column spaces of a matrix Z is the set of all linear combinations of the columns in Z. If Z = [a1, .... , an], then Col Z = Span {a1, ...., an}
See also row space.
Tell me how it was
whereat he wondered greatly, and rejoiced and at last asked me,
master!" So we mounted an elephant and fared until we came to the
greatly; then carrying away as many as he wanted he returned with
said, "O my son, thou.html">thou.html">thou.html">thou hast shown us the way to great gain,
sake and before His face! The elephants used to destroy many of
sorivellos; but Allah hath preserved thee from them, and thou
master," replied I, "God free thy neck from the fire! And do thou
country.html">country.html">country." "Yes" quoth he, "thou shalt have that permission. But
quarters to buy up these ivories. The time is drawing near; and,
their charge and will give thee wherewithal to reach thy home."
respect and honour, for some days, when the merchants came as he
made their preparations to return, my master came to me and said,
thy country." They had bought a number of tusks which they had
sent me with them, paying for my passage and settling all my
out and voyaged from island.html">island to island till we had crossed the sea
brought out and sold their stores: I also sold what I had at a
place for presents and beautiful rareties and everything else I
and crossed the deserts from country to country till I reached
kissing hands, informed him of all that had befallen me;
and he bade my story.html">story be written in letters of gold. I then
end of the history that happened to me during my seven voyages.
in Heaven and Earth!--
Now when Shahrazad had ended her story of the two.
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