Suppose e₁, ..., em is an orthonormal list of vectors in V. Let v € V. Prove that ||v||² = |(v, e₁) |² + ... + |(v, em) |² if and only if v € span(e₁, ..., em).
Suppose e₁, ..., em is an orthonormal list of vectors in V. Let v € V. Prove that ||v||² = |(v, e₁) |² + ... + |(v, em) |² if and only if v € span(e₁, ..., em).
Suppose e₁, ..., em is an orthonormal list of vectors in V. Let v € V. Prove that ||v||² = |(v, e₁) |² + ... + |(v, em) |² if and only if v € span(e₁, ..., em).
Transcribed Image Text:Suppose e₁, ..., em is an orthonormal list of vectors in V. Let v € V.
Prove that
||v||² = |(v, e₁)|² + ... + |(v₂ em) | ²
if and only if ve span(e₁, ..., em).
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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