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7 results for “vectors”

Formulae (7)

\cos\theta = \frac{A \cdot B}{\|A\|\|B\|}

Measures similarity between two vectors by the angle between them.

\vec{a}\cdot\vec{b} = \sum_i a_i b_i = |a||b|\cos\theta

Scalar product of two vectors.

|\vec{a}\times\vec{b}| = |a||b|\sin\theta

Magnitude of the vector perpendicular to two vectors.

A\vec{v} = \lambda\vec{v}

Defines eigenvalues and eigenvectors of a matrix.

\mathbf{a}\cdot\mathbf{b} = \sum a_i b_i

Sum of componentwise products of two vectors.

\cos\theta = \frac{\mathbf{a}\cdot\mathbf{b}}{\|a\|\|b\|}

Angle from the dot product and magnitudes.

\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})

Volume of the parallelepiped spanned by three vectors.