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rubygerbil291
Lv1
16 Feb 2023
Let B-b, . .. bn) be a basis for a vector space V. Explain why the B-coordinate vectors of bi ,..., bn are the columns e1 . ⦠en of the n à n identity matrix
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Jean Keeling
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17 Feb 2023
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17 Feb 2023
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Let B = {b1, b2,... bn} be an ordered basis for vector space V. Show that every inner-product on V can be computed using the values ai, j = (bj|bi) i = 1,..., n, j = 1,..., n. Hint: Take x, y V and write them as linear combinations of bi's (i = 1,..., n). Form the inner prod (x|y) and the coordinates matrices of x and y in the ordered basis B, [x] B and [y] B. Show that (x|y) = [y] B A [x] B, where n times n matrix A = [ai, j] consists of the inner products of the vectors in ordered basis B.
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Let B = {b1, b2,... bn} be an ordered basis for vector space V. Show that every inner-product on V can be computed using the values ai, j = (bj|bi) i = 1,..., n, j = 1,..., n. Hint: Take x, y V and write them as linear combinations of bi's (i = 1,..., n). Form the inner prod (x|y) and the coordinates matrices of x and y in the ordered basis B, [x] B and [y] B. Show that (x|y) = [y] B A [x] B, where n times n matrix A = [ai, j] consists of the inner products of the vectors in ordered basis B.
orchidgnu700
A 7. (7 points) Let B(b,.. ., bn) be a basis for a vector space V. Show that the coordinate mapping x-? [X]B Is one-to-one. (You may not use the theorem that states this.)
Let V be a vector space with ordered bases B and B'. Find the coordinate vector [v]B given the following matrix and the vector v = - 2b1 + 4b2 - 5b3.
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Let V be a vector space with ordered bases B and B'. Find the coordinate vector [v]B given the following matrix and the vector v = - 2b1 + 4b2 - 5b3.
tansea-lion817
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