Square Roots of Matrices and Operators
If A is a positive-definite matrix or operator, then there exists precisely one positive definite matrix or operator B with B2 = A; we then define A1/2 = √A = B. In general matrices may have multiple square roots or even an infinitude of them. For example the 2×2 identity matrix has an infinity of square roots.
Read more about this topic: Square Root
Famous quotes containing the words square and/or roots:
“A man who is good enough to shed his blood for his country is good enough to be given a square deal afterwards. More than that no man is entitled to, and less than that no man shall have.”
—Theodore Roosevelt (1858–1919)
“The Plains are not forgiving. Anything that is shallow—the easy optimism of a homesteader; the false hope that denies geography, climate, history; the tree whose roots don’t reach ground water—will dry up and blow away.”
—Kathleen Norris (b. 1947)