Multiplying a matrix by its transpose
An earlier post claimed that there practical advantages to partitioning a matrix, thinking of the matrix as a matrix of matrices. This post will give an example. Let M be a square matrix and suppose we need to multiply M by its transpose MT. We can compute this product faster than
Read moreA bit-twiddling marvel
Pop quiz: what does the following code do? bool is_leap_year_fast(uint32_t y) { return ((y * 1073750999) & 3221352463) <= 126976; } It determines whether the year y is a leap year in the Gregorian calendar, of course. :) It’s very efficient, though I don’t image that would ever matter. But
Read moreCEO Update: Exploration and experimentation for bold evolution
As we envision what the ideal future version of Stack Overflow looks like, we’re committed to engaging with our community.
Read moreBrex partners with former competitor Zip, with an eye on reducing cash burn to get to an IPO
Brex has once again made the surprising, but perhaps realistic, decision to partner with another one-time competitor. This time Zip, the CEOs of both companies told TechCrunch exclusively. In April 2022, fintech Brex announced it was making “a big push” into both the enterprise and software. The news was notable
Read moreSouth Loop Ventures closes $21M fund in Houston to build up local tech ecosystem
South Loop Ventures, a Houston-based venture firm, announced a $21 million Fund I, with Rice Management Company and Chevron Technology Ventures serving as anchor investors. The firm, which launched in 2022, focuses on seed and pre-seed companies, with $400,000 as the average check size. It also primarily hopes to focus
Read moreAlation acquires Numbers Station to bolster its AI agent offerings
Alation plans to integrate Numbers Station's products into its own as soon as the end of this quarter, Alation co-founder and CEO Satyen Sangani told TechCrunch.
Read moreSparkCharge raises $30M to help fleets electrify without commitments
SparkCharge raised $15.5 million in equity and secured a $15 million loan to expand its fleet charging operations.
Read moreSparkCharge raises $30M to help fleets electrify without commitments
SparkCharge raised $15.5 million in equity and secured a $15 million loan to expand its fleet charging operations.
Read moreOpenAI’s Codex is part of a new cohort of agentic coding tools
Last Friday, OpenAI introduced a new coding system called Codex, designed to perform complex programming tasks from natural language commands. Codex moves OpenAI into a new cohort of agentic coding tools that is just beginning to take shape. From GitHub’s early Copilot to contemporary tools like Cursor and Windsurf, most
Read moreMatrices of Matrices
It’s often useful to partition a matrix, thinking of it as a matrix whose entries are matrices. For example, you could look at the matrix 6 × 6 as a 2 × 2 matrix whose entries are 3 × 3 matrices. M is not a diagonal matrix of real numbers,
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