Suppose a new user’s data that comes in, which is stored in the vector r. Your colleague, a computer scientist, wants to apply an ‘algorithm’ on their ‘computer’ to extract extra information from r. They propose something called ‘deep heart rate parameters’ by solving for z in the problem: r = [H I] z (a) What is the dimensionality of I in this expression. (b) You tell them this idea does not convey any value and is conceptually problematic. Why? Use at most 3 sentences with linear algebraic concepts.
Suppose a new user’s data that comes in, which is stored in the vector r. Your colleague, a computer
scientist, wants to apply an ‘algorithm’ on their ‘computer’ to extract extra information from r. They
propose something called ‘deep heart rate parameters’ by solving for z in the problem:
r = [H I] z
(a) What is the dimensionality of I in this expression.
(b) You tell them this idea does not convey any value and is conceptually problematic. Why? Use at most 3 sentences with linear algebraic concepts.
(a) The dimensionality of vector I in the expression r = [H I]z is determined by the number of columns in matrix [H I]. Specifically, it's the number of rows in I, which is equal to the number of columns in [H I].
To clarify further, the expression r = [H I]z suggests that H and I are matrices, where H represents one part of the data, and I represents another part of the data, and z is a vector of parameters. In this context:
- The number of rows in the matrix [H I] is the number of rows in H (assuming both H and I have the same number of rows).
- The number of columns in [H I] is the sum of the number of columns in H and the number of columns in I.
Therefore, the dimensionality of vector I is determined by the number of columns in the matrix [H I], which is the sum of the columns in H and I, not the number of elements in I. My previous explanation was inaccurate, and I apologize for any confusion.
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