1. Two likelihood functions are equivalent if one is a scalar multiple of the other. 2. Sums and scalar multiples of skew-symmetric matrices are again skew-symmetric. 3. For example, take the scalar multiples of the identity matrix by integer powers of 2. 4. Since is unitary, this scalar multiple is uniquely determined and hence such an operator is unique. 5. A nonzero scalar multiple of an identity matrix is called a " scalar " matrix. 6. A one dimensional vector subspace consists of a non-zero vector and all of its scalar multiples . 7. (which arises in probability theory as a scalar multiple of the imaginary unit is enclosed within the curve. 8. This f _ { \ lambda } ( \ theta ) is the scalar multiple mentioned in the previous paragraph. 9. After all, any scalar multiple of some original "'? "'would also satisfy the equation. 10. This implies, among other things, that the Fubini Study metric remains unchanged up to a scalar multiple under the Ricci flow.
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