Linear Algebra with NumPy Primer Flashcards
What does this mean?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/222/q_image_thumb.png?1623104851)
the set of all real-valued matrices with n rows and d columns
What is this called? What does it mean?
1(x)
- binary indicator function,
- returns 1 if x is a true boolean and 0 otherwise
What does this mean?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/213/q_image_thumb.png?1623104826)
the set of all real-valued n-dimensional vectors
What does this mean?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/072/855/q_image_thumb.png?1623104732)
the set of real numbers
What is this?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/308/q_image_thumb.png?1623105160)
- A pair of input vector and output scalar
- The superscript indicates the index of this pair, not the exponent. In other words, x(5) is the input vector at index 5, not x raised to the power of 5.
What is this?
|C|
- Determinant if C is a matrix
- Cardinality (number of member elements) if C is a set.
What’s a column vector?
Each entry occupies one row.
What’s this?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/493/q_image_thumb.png?1623105322)
One use: denotes the i-th entry of a column vector
What does this mean?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/530/q_image_thumb.png?1623105413)
Row vector. Each entry covers 1 column
For matrix A, what is
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/696/q_image_thumb.png?1623105622)
denotes the i-th row of A
For matrix A, what is
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/619/q_image_thumb.png?1623105599)
denotes the i-th column of A
What can dot product be applied to? What’s the formula?
Two vectors of same dimensions
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/755/a_image_thumb.png?1623105814)
What’s the inner product?
Same as dot product
- What can outer product be applied to?
- What does it result in?
- What’s the formula?
- Vectors (can have different number of elements)
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/834/a_image_thumb.png?1623106039)
What’s another way to express a dot product for two column vectors x and y?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/073/976/a_image_thumb.png?1623106295)
What’s this for two vectors x and y?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/074/201/q_image_thumb.png?1623106520)
The outer product
What’s a matrix-vector product?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/075/903/a_image_thumb.png?1623106742)
- What are the properties of matrix multiplication? (2)
- What properties does it not have? (1)
Matrix multiplication is:
- associative, (AB)C=A(BC)
- distributive, A(B+C)=AB+AC
Is not:
- commutative, AB≠BA
What’s a property of transposes?
![](https://s3.amazonaws.com/brainscape-prod/system/cm/348/077/769/a_image_thumb.png?1623106969)
What’s the Hadamard product?
elementwise matrix multiplication