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this lecture is part of an online course on league groups and will be about the baker campbell house store formula so what does this formula say well suppose a and b are n by n matrices over say the reals then as we saw in the last lecture you can try writing x with a times x for b to be x of a plus b except that because a and b dont commute in general this formula doesnt actually hold and you need to add in a correction term and then you need to add in further higher order correction terms oops and so on and um what you notice is that all the terms ive written down here can be expressed um using the matrices a b we started with and just the lead bracket it would be quite trivial to write down a formula like this if were allowed to multiply matrices together however the key point of the baker campbell house door formula is that this expression here only involves the lead bracket it converges for a and b small in some sense in other words near in some neighborhood of zero but um it