Vectors Flashcards

(9 cards)

1
Q

What is a vector?

A

A vector is an element of a vector space, represented as an ordered list of numbers indicating magnitude and direction.

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2
Q

What does it mean for two vectors to be linearly independent?

A

Two vectors are linearly independent if one cannot be expressed as a scalar multiple of the other.

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3
Q

How do you calculate the Euclidean (L2) norm of a vector v = [x, y]?

A

‖v‖₂ = √(x² + y²)

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4
Q

How do you calculate the L1 norm of a vector v = [x, y]?

A

‖v‖₁ = |x| + |y|

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5
Q

What does the dot product of two vectors represent?

A

The dot product measures how much one vector projects onto another. If the dot product is zero, the vectors are orthogonal.

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6
Q

What is the formula for the dot product of u = [x₁, y₁, z₁] and v = [x₂, y₂, z₂]?

A

u ⋅ v = x₁x₂ + y₁y₂ + z₁z₂

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7
Q

How do you calculate the angle θ between two vectors?

A

cos(θ) = (u ⋅ v) / (‖u‖ ‖v‖), and θ = cos⁻¹(result).

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8
Q

How do you perform the cross product of two 3D vectors u and v?

A

Use the determinant formula:
u × v =
|i j k |
|uₓ uᵧ u𝓏|
|vₓ vᵧ v𝓏 |

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9
Q
A
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